Force is an interaction between two objects that causes one to accelerate relative to the other. It is typically caused by contact or gravitational attraction, and it is measured in Newtons (\(\text{N}\)). In order to understand how forces affect motion, one needs to understand concepts such as momentum, impulse and work. Kinematic equations are often used to calculate force based on these concepts.

The formula takes into account the initial velocity \((v_f)\) of the object, which is multiplied by the time interval \((t)\) to give the distance covered by the object in the absence of acceleration. The term \(\frac{1}{2}at^2\)takes into account the effect of acceleration on the object's position over time.

Any units for Distance, feet or meters. Dimension results are the same units. WidthDimensionWidthDegrees HeightDimensionHeightDegrees Diagonal DimensionDiagonal Degrees Show field size at a 2nd distance(like if at the background?)Show 2nd distance at units

Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results.

Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

The Angle of Field of View is independent of the field distance. The angle is computed from sensor size and focal length. The Field Distance is not limited to be only the subject or focus distance. Here it means the distance to the point where you want field size calculated. It might be the background distance for example (which then would show the Field of View at the background distance). A 2nd distance can be entered for convenience, but it is the same result as simply changing the first distance. When you specify a different embedded format (like 16:9 video on your 3:2 or 4:3 camera sensor, or a photo 4:3 format on your native 16:9 camcorder), this changes the effective sensor area and size from the format's original native value (usually a different image height), and changes the Crop Factor and the Field of View too. The calculator can show this. If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any embedded formats contained within it, so it is important to compute the correct numbers. embedded format is a complication, but it is necessary to know the sensor area used. A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Kinematics definition with example

The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results.

However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

mm Option 1 Aspect ratio uses Full Chip Native Aspect 16:9 crop in this sensor 3:2 crop in this sensor 4:3 crop in this sensor 5:4 crop in this sensor 1:1 crop in this sensor 3 Sensor Crop Factor Options 3 & 4, see theAspect Ratio sub-options 3:2,   DSLR or One Inch 16:9 in 3:2 camera 4:3 in 3:2 camera 5:4 in 3:2 camera 1:1 in 3:2 camera 4:3, compacts or phones 16:9 in 4:3 camera 3:2 in 4:3 camera 5:4 in 4:3 camera 1:1 in 4:3 camera 16:9, camcorders 4:3 in 16:9 camera 3:2 in 16:9 camera 5:4 in 16:9 camera 1:1 in 16:9 camera 5:4 camera 1:1 camera 4 Focal length of this lens Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film

These values may be very difficult to determine for phones and compact cameras and camcorders, but larger cameras likely show specification values better. Alternately, you can specify an accurate crop factor as a way to compute actual sensor size. Or Option 4 can compute Crop Factor from an accurate lens Equivalent Focal Length specifications (for a 1x sensor). The image's Exif data normally reports focal length. Use the actual real lens focal length with the actual sensor size. If you don't know focal length, the Exif data in the image file probably shows it (zoom lens focal length changes with zoom). The image Exif data may show some what you need to know to obtain some of the required information about your cell phone or compact camera to operate this calculator. Determining this otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help. The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers.

The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

After choosing the equation, rearrange it to solve for the unknown variable. Make sure you isolate the variable you want to solve for on one side of the equation and everything else on the other side. This may require some algebraic manipulation, so make sure you have a solid understanding of algebraic concepts as well.

Kinematics examples

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Full Chip Native Aspect 16:9 crop in this sensor 3:2 crop in this sensor 4:3 crop in this sensor 5:4 crop in this sensor 1:1 crop in this sensor 3 Sensor Crop Factor Options 3 & 4, see theAspect Ratio sub-options 3:2,   DSLR or One Inch 16:9 in 3:2 camera 4:3 in 3:2 camera 5:4 in 3:2 camera 1:1 in 3:2 camera 4:3, compacts or phones 16:9 in 4:3 camera 3:2 in 4:3 camera 5:4 in 4:3 camera 1:1 in 4:3 camera 16:9, camcorders 4:3 in 16:9 camera 3:2 in 16:9 camera 5:4 in 16:9 camera 1:1 in 16:9 camera 5:4 camera 1:1 camera 4 Focal length of this lens Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film

Kinematics meaning in Physics

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\(\begin{align}\begin{aligned} v_f &= v_0 + at \\[2ex] v_f &= 5 \text{ m/s} + (2 \text{ m/s}^2 \times 3 \text{ s}) \\[2ex] v_f &= 5 \text{ m/s} + 6 \text{ m/s}\\[2ex] v_f &= 11 \text{ m/s} \end{aligned} \end{align}\)

For example, if an object is initially moving at a velocity of \(v_0 = 5 \text{ m/s}\), and experiences a constant acceleration of \(a = 2 \mathrm{\,m/s^2}\) for a time of \(t = 3\) seconds, we can use the equation \(v_f = v_0 + at\) to find its final velocity:

The factor of \(\frac{1}{2}\) represents half of the acceleration multiplied by the time interval squared, and it represents the change in position caused by acceleration.

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As with any skill, the key to mastering kinematic equations is practice. Solve as many problems as you can and make sure you understand the solutions. This will help you identify patterns and strategies that you can use to solve more complex problems.

Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

The five kinematic equations are a set of formulas used to describe the motion of an object in one dimension, also known as linear motion. Each equation relates four variables: displacement \((\Delta x)\), initial velocity \((v_0)\), final velocity \((v_f)\), acceleration \((a)\), and time \((t)\).

Velocity is a measure of how fast an object is moving in a certain direction. It is defined as the rate of change of position over time, and is typically measured in meters per second (\(\text{m/s}^2\)). Velocity can be determined using kinematic equations such as the average velocity equation, which states that the average velocity of an object over a given time period can be calculated by taking the ratio of displacement divided by time.

Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Kinematicin physics

Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

There's also a large chart of Field of View (angular, in degrees) for many lens focal lengths and a few popular sensors on the next page. Another page is a Field of View math section if interested in that. The Depth of Field calculator here can also show Field of View size at both subject or background distances. Or somewhat related (same math), another calculator can compute distance or size of an object in a photo. First about Camera or Video format specifications This calculation requires accurate sensor size and focal length and field distance. Calculators simply MUST be told accurate numbers, else otherwise, the standard saying is "garbage in, garbage out". It will compute with the numbers you enter. That means YOU must know those numbers. All of the problems are from not knowing this accurate data. These values may be very difficult to determine for phones and compact cameras and camcorders, but larger cameras likely show specification values better. Alternately, you can specify an accurate crop factor as a way to compute actual sensor size. Or Option 4 can compute Crop Factor from an accurate lens Equivalent Focal Length specifications (for a 1x sensor). The image's Exif data normally reports focal length. Use the actual real lens focal length with the actual sensor size. If you don't know focal length, the Exif data in the image file probably shows it (zoom lens focal length changes with zoom). The image Exif data may show some what you need to know to obtain some of the required information about your cell phone or compact camera to operate this calculator. Determining this otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help. The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers. Field of View Calculator Field of View can be expressed as either the angular view or the dimensional field which can be horizontal width, vertical height, or as the diagonal. Angular field of view is commonly stated as the diagonal (which is the circular lens view). The angle is independent of distance (angle is the same at any distance). Dimensional field of view (in feet, meters, etc) is computed at one specific distance (of same units). The Field of View accuracy is dependent on the known accuracy of distance, focal length and sensor size dimensions. Zoom lenses have many focal lengths. The applicable one used for a picture is possibly determined in the image EXIF data (but that can be inaccurate, especially if internal focusing). But see a complication of precision in zoom lenses. Regardless even if Equivalent focal length is mentioned here, DON'T specify any Equivalent Focal Length as being the Focal Length actually used on your camera, because it is not. They are Not the same thing. Using Equivalent Focal Length instead of the actual real focal length will produce a huge error. The Field of View calculation necessarily uses the real focal length of your actual lens. The term Equivalent Focal Length is NOT the focal length of the lens you are using. Instead Equivalent Focal Length convention refers to a comparison to different camera with either 35 mm film or a Full Frame 1x sensor, for the focal length *IT* would use to see the same size field of view as your lens sees on your camera. This number is familiar to the oldtimers with much 35 mm film experience (and DSLR 1x crop factor sensors). Meaning, if you do specify Equivalent Focal Length here, then to have any meaning, you must also specify the corresponding 36x24 mm 1x full frame sensor size (for which Equivalent Focal Length is specified) in Option 1 or 3 to compute that Equivalent Field of View. I would trust the manufacturer's data, but whoever else specified the Equivalent may not have it right. It won't be meaningful unless you understand what it means. I do see that the Apple iPhone 14 with multiple cameras has now labeled focal lengths with the Equivalent number — the angle of view in degrees would be equivalent, but the focal length number instead applies to 35 mm film size sensors. It is very puzzling why the manufacturers specifications can't simply mention the actual numbers for the cameras sensor size and focal length, but I suppose not many users care. A cell phone camera actual main focal length IS CERTAINLY NOT NEAR 26 MM as is often told on the internet. That would seem to obviously be its "Equivalent Focal Length", meaning this phone camera has the same field of view as a 35 mm camera would have, if *IT* used that 26 mm focal length. That's just to compare its field of view for users with 35 mm film experience, but that 26 mm varies too, not all cell cameras have the same size sensor. A cell phone camera "normal" lens focal length is closer to 4 or 5 mm (± a fraction, but it depends on actual sensor size). Do be advised that a calculator will compute more garbage if given garbage data. UNITS: Field of View is computed from focal length and sensor size (both of which are always units in milimeters), and also its dimensions are computed from distance of the Field of the View. The external dimensional units of field or distance (those outside the camera) can use any units, including feet, meters, miles, km, light years or cubits, etc. I’ll just call them Units. Results will be in those same units, but YOU MUST BE CONSISTENT WITH UNITS. External distance and field size must be in the SAME units here (because the dimensional units in the similar triangle in front of the lens do cancel out if consistent). The blue numbers shown here are the computed FoV Size Result numbers. Fisheye lenses or macro or unusually close focus distances are different special cases that WILL adversely affect calculation accuracy. These special cases are NOT provided here. Macro necessarily works using size magnification (like 1:1) instead of focus distance (The focal length at 1:1 magnification is typically twice what is marked on the lens). Options 1-5 are four ways to specify sensor size here (Option 2 was deleted following improvements). It is a busy screen. Enter Focal Length and Distance, select a sensor size in Option 1-5. Then Field of View is computed from focal length, distance, and sensor size. Options 6-8 are more special purpose, but Options 6-8 still use the sensor size currently specified by Options 1-5. The Blue FLIP button at Option 6 simply toggles to swap the Focal Length and Distance parameters for 6 and 8, to specify either one and find the other. After typing text numbers here, to process the change in an active field, you can just hit the Enter key in that field, or you can use the ReCompute button. The buttons should compute automatically.

Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Native Sensor Size, Height mm mm Option 1 Aspect ratio uses Full Chip Native Aspect 16:9 crop in this sensor 3:2 crop in this sensor 4:3 crop in this sensor 5:4 crop in this sensor 1:1 crop in this sensor 3 Sensor Crop Factor Options 3 & 4, see theAspect Ratio sub-options 3:2,   DSLR or One Inch 16:9 in 3:2 camera 4:3 in 3:2 camera 5:4 in 3:2 camera 1:1 in 3:2 camera 4:3, compacts or phones 16:9 in 4:3 camera 3:2 in 4:3 camera 5:4 in 4:3 camera 1:1 in 4:3 camera 16:9, camcorders 4:3 in 16:9 camera 3:2 in 16:9 camera 5:4 in 16:9 camera 1:1 in 16:9 camera 5:4 camera 1:1 camera 4 Focal length of this lens Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film

A cell phone camera actual main focal length IS CERTAINLY NOT NEAR 26 MM as is often told on the internet. That would seem to obviously be its "Equivalent Focal Length", meaning this phone camera has the same field of view as a 35 mm camera would have, if *IT* used that 26 mm focal length. That's just to compare its field of view for users with 35 mm film experience, but that 26 mm varies too, not all cell cameras have the same size sensor. A cell phone camera "normal" lens focal length is closer to 4 or 5 mm (± a fraction, but it depends on actual sensor size). Do be advised that a calculator will compute more garbage if given garbage data. UNITS: Field of View is computed from focal length and sensor size (both of which are always units in milimeters), and also its dimensions are computed from distance of the Field of the View. The external dimensional units of field or distance (those outside the camera) can use any units, including feet, meters, miles, km, light years or cubits, etc. I’ll just call them Units. Results will be in those same units, but YOU MUST BE CONSISTENT WITH UNITS. External distance and field size must be in the SAME units here (because the dimensional units in the similar triangle in front of the lens do cancel out if consistent). The blue numbers shown here are the computed FoV Size Result numbers. Fisheye lenses or macro or unusually close focus distances are different special cases that WILL adversely affect calculation accuracy. These special cases are NOT provided here. Macro necessarily works using size magnification (like 1:1) instead of focus distance (The focal length at 1:1 magnification is typically twice what is marked on the lens). Options 1-5 are four ways to specify sensor size here (Option 2 was deleted following improvements). It is a busy screen. Enter Focal Length and Distance, select a sensor size in Option 1-5. Then Field of View is computed from focal length, distance, and sensor size. Options 6-8 are more special purpose, but Options 6-8 still use the sensor size currently specified by Options 1-5. The Blue FLIP button at Option 6 simply toggles to swap the Focal Length and Distance parameters for 6 and 8, to specify either one and find the other. After typing text numbers here, to process the change in an active field, you can just hit the Enter key in that field, or you can use the ReCompute button. The buttons should compute automatically.

Updated 29 October 2024 Field of View CalculatorField DimensionAngle of View Focal Length   mm Field Distance units Any units for Distance, feet or meters. Dimension results are the same units. WidthDimensionWidthDegrees HeightDimensionHeightDegrees Diagonal DimensionDiagonal Degrees Show field size at a 2nd distance(like if at the background?)Show 2nd distance at units 1 Native Sensor Size, WidthNative Sensor Size, Height mm mm Option 1 Aspect ratio uses Full Chip Native Aspect 16:9 crop in this sensor 3:2 crop in this sensor 4:3 crop in this sensor 5:4 crop in this sensor 1:1 crop in this sensor 3 Sensor Crop Factor Options 3 & 4, see theAspect Ratio sub-options 3:2,   DSLR or One Inch 16:9 in 3:2 camera 4:3 in 3:2 camera 5:4 in 3:2 camera 1:1 in 3:2 camera 4:3, compacts or phones 16:9 in 4:3 camera 3:2 in 4:3 camera 5:4 in 4:3 camera 1:1 in 4:3 camera 16:9, camcorders 4:3 in 16:9 camera 3:2 in 16:9 camera 5:4 in 16:9 camera 1:1 in 16:9 camera 5:4 camera 1:1 camera 4 Focal length of this lens Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film   6 6 & 8 Using Sensor Size in Option 1 3 4 5 of Same units  in the Width Height Diagonal  dimension 7 Any Field Distance is Same angle Find Focal Length for a Field of View Angle of degrees 8 x   using Feet Meters 9 Compute Sensor Size above from the measured dimensions of Field Width × Field Height (same units)actually measured in the view AT the distance and focal length specified above. This Calculator requires JavaScript be enabled in your browser The Angle of Field of View is independent of the field distance. The angle is computed from sensor size and focal length. The Field Distance is not limited to be only the subject or focus distance. Here it means the distance to the point where you want field size calculated. It might be the background distance for example (which then would show the Field of View at the background distance). A 2nd distance can be entered for convenience, but it is the same result as simply changing the first distance. When you specify a different embedded format (like 16:9 video on your 3:2 or 4:3 camera sensor, or a photo 4:3 format on your native 16:9 camcorder), this changes the effective sensor area and size from the format's original native value (usually a different image height), and changes the Crop Factor and the Field of View too. The calculator can show this. If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any embedded formats contained within it, so it is important to compute the correct numbers. embedded format is a complication, but it is necessary to know the sensor area used. A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here Copyright © 2014-2024 by Wayne Fulton - All rights are reserved.

The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers.

But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

In simpler terms, the equation means that the final velocity of an object depends on its initial velocity, how much it accelerates, and how far it travels. It can be used to calculate the final velocity of an object when its initial velocity, acceleration, and displacement are known.

Before we get into the kinematic equations, let's learn about some important kinematic variables that are used in the kinematic equations.

Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Meaning, if you do specify Equivalent Focal Length here, then to have any meaning, you must also specify the corresponding 36x24 mm 1x full frame sensor size (for which Equivalent Focal Length is specified) in Option 1 or 3 to compute that Equivalent Field of View. I would trust the manufacturer's data, but whoever else specified the Equivalent may not have it right. It won't be meaningful unless you understand what it means. I do see that the Apple iPhone 14 with multiple cameras has now labeled focal lengths with the Equivalent number — the angle of view in degrees would be equivalent, but the focal length number instead applies to 35 mm film size sensors. It is very puzzling why the manufacturers specifications can't simply mention the actual numbers for the cameras sensor size and focal length, but I suppose not many users care. A cell phone camera actual main focal length IS CERTAINLY NOT NEAR 26 MM as is often told on the internet. That would seem to obviously be its "Equivalent Focal Length", meaning this phone camera has the same field of view as a 35 mm camera would have, if *IT* used that 26 mm focal length. That's just to compare its field of view for users with 35 mm film experience, but that 26 mm varies too, not all cell cameras have the same size sensor. A cell phone camera "normal" lens focal length is closer to 4 or 5 mm (± a fraction, but it depends on actual sensor size). Do be advised that a calculator will compute more garbage if given garbage data. UNITS: Field of View is computed from focal length and sensor size (both of which are always units in milimeters), and also its dimensions are computed from distance of the Field of the View. The external dimensional units of field or distance (those outside the camera) can use any units, including feet, meters, miles, km, light years or cubits, etc. I’ll just call them Units. Results will be in those same units, but YOU MUST BE CONSISTENT WITH UNITS. External distance and field size must be in the SAME units here (because the dimensional units in the similar triangle in front of the lens do cancel out if consistent). The blue numbers shown here are the computed FoV Size Result numbers. Fisheye lenses or macro or unusually close focus distances are different special cases that WILL adversely affect calculation accuracy. These special cases are NOT provided here. Macro necessarily works using size magnification (like 1:1) instead of focus distance (The focal length at 1:1 magnification is typically twice what is marked on the lens). Options 1-5 are four ways to specify sensor size here (Option 2 was deleted following improvements). It is a busy screen. Enter Focal Length and Distance, select a sensor size in Option 1-5. Then Field of View is computed from focal length, distance, and sensor size. Options 6-8 are more special purpose, but Options 6-8 still use the sensor size currently specified by Options 1-5. The Blue FLIP button at Option 6 simply toggles to swap the Focal Length and Distance parameters for 6 and 8, to specify either one and find the other. After typing text numbers here, to process the change in an active field, you can just hit the Enter key in that field, or you can use the ReCompute button. The buttons should compute automatically.

If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Once you have read the problem, make a rough sketch of the problem. This will help you understand the nuances of the question and understand which variables are at play.

A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Now that we know what is kinematics, and its different variables, let's learn about the equations that we can use to solve various problems of motion. For this article, we'll only focus on Kinematic equations for one-dimensional motion, also known as linear motion, and learn about the formulas, their significance in physics, and how they are applied in real-life situations.

The equation states that the final velocity squared \((v_f^2)\) is equal to the initial velocity squared \((v_0^2)\) plus two times the product of the acceleration \((a)\) and the displacement \((\Delta x)\) of the object.

Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film

Updated 29 October 2024 Field of View CalculatorField DimensionAngle of View Focal Length   mm Field Distance units Any units for Distance, feet or meters. Dimension results are the same units. WidthDimensionWidthDegrees HeightDimensionHeightDegrees Diagonal DimensionDiagonal Degrees Show field size at a 2nd distance(like if at the background?)Show 2nd distance at units 1 Native Sensor Size, WidthNative Sensor Size, Height mm mm Option 1 Aspect ratio uses Full Chip Native Aspect 16:9 crop in this sensor 3:2 crop in this sensor 4:3 crop in this sensor 5:4 crop in this sensor 1:1 crop in this sensor 3 Sensor Crop Factor Options 3 & 4, see theAspect Ratio sub-options 3:2,   DSLR or One Inch 16:9 in 3:2 camera 4:3 in 3:2 camera 5:4 in 3:2 camera 1:1 in 3:2 camera 4:3, compacts or phones 16:9 in 4:3 camera 3:2 in 4:3 camera 5:4 in 4:3 camera 1:1 in 4:3 camera 16:9, camcorders 4:3 in 16:9 camera 3:2 in 16:9 camera 5:4 in 16:9 camera 1:1 in 16:9 camera 5:4 camera 1:1 camera 4 Focal length of this lens Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film   6 6 & 8 Using Sensor Size in Option 1 3 4 5 of Same units  in the Width Height Diagonal  dimension 7 Any Field Distance is Same angle Find Focal Length for a Field of View Angle of degrees 8 x   using Feet Meters 9 Compute Sensor Size above from the measured dimensions of Field Width × Field Height (same units)actually measured in the view AT the distance and focal length specified above.

Other articles where objective lens is discussed: microscope: The objective: The optics of the microscope objective are defined by the focal length, N.A., ...

Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same).

First about Camera or Video format specifications This calculation requires accurate sensor size and focal length and field distance. Calculators simply MUST be told accurate numbers, else otherwise, the standard saying is "garbage in, garbage out". It will compute with the numbers you enter. That means YOU must know those numbers. All of the problems are from not knowing this accurate data. These values may be very difficult to determine for phones and compact cameras and camcorders, but larger cameras likely show specification values better. Alternately, you can specify an accurate crop factor as a way to compute actual sensor size. Or Option 4 can compute Crop Factor from an accurate lens Equivalent Focal Length specifications (for a 1x sensor). The image's Exif data normally reports focal length. Use the actual real lens focal length with the actual sensor size. If you don't know focal length, the Exif data in the image file probably shows it (zoom lens focal length changes with zoom). The image Exif data may show some what you need to know to obtain some of the required information about your cell phone or compact camera to operate this calculator. Determining this otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help. The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers. Field of View Calculator Field of View can be expressed as either the angular view or the dimensional field which can be horizontal width, vertical height, or as the diagonal. Angular field of view is commonly stated as the diagonal (which is the circular lens view). The angle is independent of distance (angle is the same at any distance). Dimensional field of view (in feet, meters, etc) is computed at one specific distance (of same units). The Field of View accuracy is dependent on the known accuracy of distance, focal length and sensor size dimensions. Zoom lenses have many focal lengths. The applicable one used for a picture is possibly determined in the image EXIF data (but that can be inaccurate, especially if internal focusing). But see a complication of precision in zoom lenses. Regardless even if Equivalent focal length is mentioned here, DON'T specify any Equivalent Focal Length as being the Focal Length actually used on your camera, because it is not. They are Not the same thing. Using Equivalent Focal Length instead of the actual real focal length will produce a huge error. The Field of View calculation necessarily uses the real focal length of your actual lens. The term Equivalent Focal Length is NOT the focal length of the lens you are using. Instead Equivalent Focal Length convention refers to a comparison to different camera with either 35 mm film or a Full Frame 1x sensor, for the focal length *IT* would use to see the same size field of view as your lens sees on your camera. This number is familiar to the oldtimers with much 35 mm film experience (and DSLR 1x crop factor sensors). Meaning, if you do specify Equivalent Focal Length here, then to have any meaning, you must also specify the corresponding 36x24 mm 1x full frame sensor size (for which Equivalent Focal Length is specified) in Option 1 or 3 to compute that Equivalent Field of View. I would trust the manufacturer's data, but whoever else specified the Equivalent may not have it right. It won't be meaningful unless you understand what it means. I do see that the Apple iPhone 14 with multiple cameras has now labeled focal lengths with the Equivalent number — the angle of view in degrees would be equivalent, but the focal length number instead applies to 35 mm film size sensors. It is very puzzling why the manufacturers specifications can't simply mention the actual numbers for the cameras sensor size and focal length, but I suppose not many users care. A cell phone camera actual main focal length IS CERTAINLY NOT NEAR 26 MM as is often told on the internet. That would seem to obviously be its "Equivalent Focal Length", meaning this phone camera has the same field of view as a 35 mm camera would have, if *IT* used that 26 mm focal length. That's just to compare its field of view for users with 35 mm film experience, but that 26 mm varies too, not all cell cameras have the same size sensor. A cell phone camera "normal" lens focal length is closer to 4 or 5 mm (± a fraction, but it depends on actual sensor size). Do be advised that a calculator will compute more garbage if given garbage data. UNITS: Field of View is computed from focal length and sensor size (both of which are always units in milimeters), and also its dimensions are computed from distance of the Field of the View. The external dimensional units of field or distance (those outside the camera) can use any units, including feet, meters, miles, km, light years or cubits, etc. I’ll just call them Units. Results will be in those same units, but YOU MUST BE CONSISTENT WITH UNITS. External distance and field size must be in the SAME units here (because the dimensional units in the similar triangle in front of the lens do cancel out if consistent). The blue numbers shown here are the computed FoV Size Result numbers. Fisheye lenses or macro or unusually close focus distances are different special cases that WILL adversely affect calculation accuracy. These special cases are NOT provided here. Macro necessarily works using size magnification (like 1:1) instead of focus distance (The focal length at 1:1 magnification is typically twice what is marked on the lens). Options 1-5 are four ways to specify sensor size here (Option 2 was deleted following improvements). It is a busy screen. Enter Focal Length and Distance, select a sensor size in Option 1-5. Then Field of View is computed from focal length, distance, and sensor size. Options 6-8 are more special purpose, but Options 6-8 still use the sensor size currently specified by Options 1-5. The Blue FLIP button at Option 6 simply toggles to swap the Focal Length and Distance parameters for 6 and 8, to specify either one and find the other. After typing text numbers here, to process the change in an active field, you can just hit the Enter key in that field, or you can use the ReCompute button. The buttons should compute automatically.

This equation \((\Delta x = \frac{1}{2}(v_0 + v_f)t)\) relates to the displacement \((\Delta x)\) of an object moving with a constant acceleration, given its initial velocity \((v_0)\), final velocity \((v_f)\) and time \((t)\) of motion.

Kinematic formulas are used to solve problems involving one-dimensional motion. These problems may include finding the displacement, velocity, acceleration, or time of an object.

Field Distance units Any units for Distance, feet or meters. Dimension results are the same units. WidthDimensionWidthDegrees HeightDimensionHeightDegrees Diagonal DimensionDiagonal Degrees Show field size at a 2nd distance(like if at the background?)Show 2nd distance at units

Kinematic equations are mathematical equations that describe the motion of objects. They are derived from the equations of motion, which are a set of laws that describe how objects move.

The equation is derived from the kinematic equations of motion, which describe the motion of objects in terms of their position, velocity, acceleration, and time. In this specific equation, the final velocity is equal to the initial velocity plus the product of acceleration and time.

A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film

The image Exif data may show some what you need to know to obtain some of the required information about your cell phone or compact camera to operate this calculator. Determining this otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help. The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers.

Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

By following these tips, you can become proficient in solving kinematic equation problems and score well on exams. Remember to always start by understanding the concepts, identify the variables, choose the right formula, rearrange the equation, plug in the values, and practice. With time and practice, you can master the art of kinematic equations and tackle even the most complex physics problems with ease.

Understanding kinematic equations is crucial for anyone studying physics or interested in understanding the basic principles of motion. By following the tips outlined in this article and practising with examples, you can become proficient in solving problems involving kinematic equations. Remember to always identify the variables given in the problem, use the appropriate equation, rearrange the equation to solve for the unknown variable, and plug in the values of the known variables. With practice, you can master the art of kinematic equations and tackle even the most complex physics problems with ease.

Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Kinematics Class 11

Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Momentum is defined as mass times velocity, and it determines how much “punch” a moving body has against another body when they collide or interact with each other. Momentum remains constant unless external forces act upon it, meaning that if two objects have equal masses but different velocities then they will have different momentums; similarly, if two objects have equal velocities but different masses then their momentums will also be different. Kinematic equations such as conservation of momentum can therefore help us understand interactions between moving bodies, allowing us to predict their behaviour after impacts or collisions occur.

The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

In multiphoton excitation microscopy, fluorescent dyes are excited by absorbing the energy of two photons simultaneously. The dyes are excited at twice the ...

How to pronounce Kinematics

The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC.

Kinematics vs Kinetics

When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

This calculator tool computes the Field of View seen by your camera and lens. Field of View is an angle which depends on the focal length and sensor size, but the calculator also computes dimensional Field of View sizes (width, height, or diagonal fields) at some specific distance, like at the subject distance, and another, like at a background distance. We don't always care about precise field size, but suppose you plan a portrait to include a 2x3 foot subject area. You should know you need to stand back six or eight feet for proper portrait perspective. What focal length is that field size and distance going to require? (Option 6, and it depends on your sensor size). And the background may be six feet farther back yet, then how large does it have to be? This calculator can plan or verify your choice. More usage descriptions are below the calculator. There's also a large chart of Field of View (angular, in degrees) for many lens focal lengths and a few popular sensors on the next page. Another page is a Field of View math section if interested in that. The Depth of Field calculator here can also show Field of View size at both subject or background distances. Or somewhat related (same math), another calculator can compute distance or size of an object in a photo. First about Camera or Video format specifications This calculation requires accurate sensor size and focal length and field distance. Calculators simply MUST be told accurate numbers, else otherwise, the standard saying is "garbage in, garbage out". It will compute with the numbers you enter. That means YOU must know those numbers. All of the problems are from not knowing this accurate data. These values may be very difficult to determine for phones and compact cameras and camcorders, but larger cameras likely show specification values better. Alternately, you can specify an accurate crop factor as a way to compute actual sensor size. Or Option 4 can compute Crop Factor from an accurate lens Equivalent Focal Length specifications (for a 1x sensor). The image's Exif data normally reports focal length. Use the actual real lens focal length with the actual sensor size. If you don't know focal length, the Exif data in the image file probably shows it (zoom lens focal length changes with zoom). The image Exif data may show some what you need to know to obtain some of the required information about your cell phone or compact camera to operate this calculator. Determining this otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help. The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers. Field of View Calculator Field of View can be expressed as either the angular view or the dimensional field which can be horizontal width, vertical height, or as the diagonal. Angular field of view is commonly stated as the diagonal (which is the circular lens view). The angle is independent of distance (angle is the same at any distance). Dimensional field of view (in feet, meters, etc) is computed at one specific distance (of same units). The Field of View accuracy is dependent on the known accuracy of distance, focal length and sensor size dimensions. Zoom lenses have many focal lengths. The applicable one used for a picture is possibly determined in the image EXIF data (but that can be inaccurate, especially if internal focusing). But see a complication of precision in zoom lenses. Regardless even if Equivalent focal length is mentioned here, DON'T specify any Equivalent Focal Length as being the Focal Length actually used on your camera, because it is not. They are Not the same thing. Using Equivalent Focal Length instead of the actual real focal length will produce a huge error. The Field of View calculation necessarily uses the real focal length of your actual lens. The term Equivalent Focal Length is NOT the focal length of the lens you are using. Instead Equivalent Focal Length convention refers to a comparison to different camera with either 35 mm film or a Full Frame 1x sensor, for the focal length *IT* would use to see the same size field of view as your lens sees on your camera. This number is familiar to the oldtimers with much 35 mm film experience (and DSLR 1x crop factor sensors). Meaning, if you do specify Equivalent Focal Length here, then to have any meaning, you must also specify the corresponding 36x24 mm 1x full frame sensor size (for which Equivalent Focal Length is specified) in Option 1 or 3 to compute that Equivalent Field of View. I would trust the manufacturer's data, but whoever else specified the Equivalent may not have it right. It won't be meaningful unless you understand what it means. I do see that the Apple iPhone 14 with multiple cameras has now labeled focal lengths with the Equivalent number — the angle of view in degrees would be equivalent, but the focal length number instead applies to 35 mm film size sensors. It is very puzzling why the manufacturers specifications can't simply mention the actual numbers for the cameras sensor size and focal length, but I suppose not many users care. A cell phone camera actual main focal length IS CERTAINLY NOT NEAR 26 MM as is often told on the internet. That would seem to obviously be its "Equivalent Focal Length", meaning this phone camera has the same field of view as a 35 mm camera would have, if *IT* used that 26 mm focal length. That's just to compare its field of view for users with 35 mm film experience, but that 26 mm varies too, not all cell cameras have the same size sensor. A cell phone camera "normal" lens focal length is closer to 4 or 5 mm (± a fraction, but it depends on actual sensor size). Do be advised that a calculator will compute more garbage if given garbage data. UNITS: Field of View is computed from focal length and sensor size (both of which are always units in milimeters), and also its dimensions are computed from distance of the Field of the View. The external dimensional units of field or distance (those outside the camera) can use any units, including feet, meters, miles, km, light years or cubits, etc. I’ll just call them Units. Results will be in those same units, but YOU MUST BE CONSISTENT WITH UNITS. External distance and field size must be in the SAME units here (because the dimensional units in the similar triangle in front of the lens do cancel out if consistent). The blue numbers shown here are the computed FoV Size Result numbers. Fisheye lenses or macro or unusually close focus distances are different special cases that WILL adversely affect calculation accuracy. These special cases are NOT provided here. Macro necessarily works using size magnification (like 1:1) instead of focus distance (The focal length at 1:1 magnification is typically twice what is marked on the lens). Options 1-5 are four ways to specify sensor size here (Option 2 was deleted following improvements). It is a busy screen. Enter Focal Length and Distance, select a sensor size in Option 1-5. Then Field of View is computed from focal length, distance, and sensor size. Options 6-8 are more special purpose, but Options 6-8 still use the sensor size currently specified by Options 1-5. The Blue FLIP button at Option 6 simply toggles to swap the Focal Length and Distance parameters for 6 and 8, to specify either one and find the other. After typing text numbers here, to process the change in an active field, you can just hit the Enter key in that field, or you can use the ReCompute button. The buttons should compute automatically.

dimension 7 Any Field Distance is Same angle Find Focal Length for a Field of View Angle of degrees 8 x   using Feet Meters 9 Compute Sensor Size above from the measured dimensions of Field Width × Field Height (same units)actually measured in the view AT the distance and focal length specified above.

The equation \((\Delta x = v_ft - \frac{1}{2}at^2)\) is a formula used to calculate the displacement or change in position \((\Delta x)\) of an object that is moving with a constant acceleration \((a)\) over a certain amount of time \((t)\).

One common misconception is that kinematic formulas only apply to objects moving in a straight line. However, they can also be applied to objects moving in a curved path.

The equation \((v_f^2 = v_0^2 + 2a \Delta x)\) is a kinematic equation that relates the final velocity \((v_f)\) of an object to its initial velocity \((v_0)\), acceleration \((a)\) and displacement \((\Delta x)\).

The Angle of Field of View is independent of the field distance. The angle is computed from sensor size and focal length. The Field Distance is not limited to be only the subject or focus distance. Here it means the distance to the point where you want field size calculated. It might be the background distance for example (which then would show the Field of View at the background distance). A 2nd distance can be entered for convenience, but it is the same result as simply changing the first distance. When you specify a different embedded format (like 16:9 video on your 3:2 or 4:3 camera sensor, or a photo 4:3 format on your native 16:9 camcorder), this changes the effective sensor area and size from the format's original native value (usually a different image height), and changes the Crop Factor and the Field of View too. The calculator can show this. If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any embedded formats contained within it, so it is important to compute the correct numbers. embedded format is a complication, but it is necessary to know the sensor area used. A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here Copyright © 2014-2024 by Wayne Fulton - All rights are reserved.

When you specify a different embedded format (like 16:9 video on your 3:2 or 4:3 camera sensor, or a photo 4:3 format on your native 16:9 camcorder), this changes the effective sensor area and size from the format's original native value (usually a different image height), and changes the Crop Factor and the Field of View too. The calculator can show this. If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any embedded formats contained within it, so it is important to compute the correct numbers. embedded format is a complication, but it is necessary to know the sensor area used. A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Before you can start solving kinematic equation problems, it is important to have a solid understanding of the concepts involved. Make sure you understand the definitions of terms such as displacement, velocity, acceleration, and time. Knowing the basics is crucial for tackling more complex problems.

Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Kinematics is an integral part of physics that deals with the study of motion. It examines how objects move and change their positions over time, as well as the forces that cause these motions. This field of study looks at velocity, acceleration, displacement, and other related concepts to help explain how things move in the physical world. Learning about kinematics can provide a foundation for understanding more advanced topics in physics such as momentum, energy conservation, work-energy theorem and many more. Furthermore, kinematic equations are used to solve problems involving motion which makes it an important tool for problem-solving in O-level Physics exams.

Geniebook's science teachers have prepared a set of practice questions for those interested in solving problems related to kinematic equations. You can access the questions and hone your skills by clicking here.

Energy refers to the capacity for doing work, and it comes in many forms including potential energy, kinetic energy and thermal energy. Potential energy is stored energy due to an object’s position relative to other objects while kinetic energy reflects the motion of an object through space. Thermal energy refers to the heat generated from chemical reactions or friction between moving objects. Kinematic equations such as the Work-Energy Theorem allow us to calculate both kinetic and potential energies associated with a given system of objects.

But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

The equation \((\Delta x={v_0}t + \frac{1}{2}at^2)\) relates to the displacement \((\Delta x)\) of an object that is moving with a constant acceleration \((a)\) over a period of time \((t)\), starting with an initial velocity \((v_0)\).

The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Dec 27, 2022 — Space charge polarization • When an electric field is applied to a bulk dielectric material the.

Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Another misconception is that kinematic formulas can only be used to solve problems involving constant acceleration. However, they can also be used to solve problems involving non-uniform acceleration.

Uniform acceleration occurs when the acceleration of an object remains constant over time, while non-uniform acceleration occurs when the acceleration of an object changes over time.

In simpler terms, the equation describes how the displacement of an object changes over time when it is subjected to a constant acceleration.

Width Height Diagonal  dimension 7 Any Field Distance is Same angle Find Focal Length for a Field of View Angle of degrees 8 x   using Feet Meters 9 Compute Sensor Size above from the measured dimensions of Field Width × Field Height (same units)actually measured in the view AT the distance and focal length specified above.

If using options 1 to 4, do pay attention to properly specify Aspect Ratio. The crop factor determines sensor Size, and then native aspect ratio specifies the Shape of it. This in turn specifies the size of any embedded formats contained within it, so it is important to compute the correct numbers. embedded format is a complication, but it is necessary to know the sensor area used. A red warning may be shown if the Aspect Ratio specified does not match the native Crop Factor computed in Option 3 or 4 (native Aspect Ratio in Option 1 or 5 is computed from actual sensor size). The warning means that an aspect ratio with the correct base aspect ratio (the native sensor size) was likely not selected, which seems an easy oversight, not likely intended, but mistakes change active sensor size and the DOF numbers. Verify, but the warning can be ignored if it's actually correct (you could let me know about the facts of that situation). But meaning, if you select a 16:9 movie aspect ratio in a 4:3 camera, this correct aspect ratio selection specifies both, as "16:9 in 4:3 camera". The warning makes the standard assumption that native crop factors less than 2x should be 3:2, or equal or larger than 2x should be 4:3 (with exception for 2.7x), which are the normal expected and required camera values. Actually, I use 1.9x as that warning boundary. Rounding: Four or five significant digits may be shown, but inputs of focal length or distance or sensor size or aspect ratio values are rounded values, not that precise (the math is accurate, but camera specifications round things). In math, the final answer can only contain as many significant digits as the least precise value. Only couple of significant digits is not very precise, but should be somewhat close. Still multiplying a 5 mm sensor width into a 30 foot field width multiplies any error too. Excessive digits are shown just in case those results are reentered to recompute back to original values, avoiding additional round-off (for example in Option 9). That's just my whim to aid verifying all results are accurate. But for example, if you might claim the calculator does not compute your precisely measured field dimensions, then use them in Option 9 to compute your computed sensor size. It is simple geometry, except distance is normally a guessed value, and focal lengths are approximated rounded values. And also, the focal length marked on the lens is when focused at infinity. It generally becomes longer at close focus distances, except internal focusing can change focal length to other values. And zoom lenses report focal length in steps, not with full precision. Magnification of field size from sensor size can also compute actual focal length. But these rounded issues are generally not much problem for routine Field of View work. Knowing the accurate distance to the field is usually the main problem. Accepted Ft' In" InputValue 88 8.258.25 8' 6"8.5 8 6.58.542 8.1' 6.25"8.621 Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Displacement is the change in the position of an object in one dimension. It is represented by the symbol Δx and is measured in meters.

Speed is the rate at which an object moves. On the other hand, velocity is the rate at which an object moves in a specific direction.

In other words, the equation provides a way to calculate the change in position of an object when it starts with a certain velocity, undergoes acceleration and then ends with a different velocity. The equation assumes that the acceleration remains constant throughout the motion.

Mar 7, 2023 — The diagram below shows Abbe error from rotation about the pitch axis, when the point of interest is coaxial with the Z or yaw axis. In this ...

Positive acceleration occurs when the velocity of an object increases in the direction of its initial motion, while negative acceleration occurs when the velocity of an object decreases in the direction of its initial motion.

If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC.

Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Options 3 & 4, see theAspect Ratio sub-options 3:2,   DSLR or One Inch 16:9 in 3:2 camera 4:3 in 3:2 camera 5:4 in 3:2 camera 1:1 in 3:2 camera 4:3, compacts or phones 16:9 in 4:3 camera 3:2 in 4:3 camera 5:4 in 4:3 camera 1:1 in 4:3 camera 16:9, camcorders 4:3 in 16:9 camera 3:2 in 16:9 camera 5:4 in 16:9 camera 1:1 in 16:9 camera 5:4 camera 1:1 camera 4 Focal length of this lens Equivalent focal length on 35 mm film or 1x sensor mm mm 5 Film andSensor Size Description Mostly this is Film Size. For CCD sensors, it will show approximate WxH mm dimensions 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" CCD iPhone 5 1/3" CCD iPhone 5S, 6, f=4.2 mm 1/3" CCD iPhone 7 f=4 mm 1/2.9" CCD Sony Exmor 1/2.55" CCD iPhone XR, XS f=4.25 mm iPhone 13 f=5.7 mm 1/2.6" CCD Samsung 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD Nikon, Sony, Pentax, Panasonic 1/2.3" CCD Sony Exmor 1/2" CCD 1/1.8" CCD 1/1.7" CCD Canon 1/1.7" CCD Pentax 1/1.6" CCD 2/3” CCD Fuji, Nokia 1/1.2" CCD One Inch, CX 2.7x crop Four Thirds 2x Olympus, Panasonic Foveon Sigma Canon APS-C 1.6x crop Canon APS-H 1.3x crop Canon full frame, 1x crop APS-C 1.5x crop Nikon DX, Sony APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop Nikon, Sony, full frame 1x crop Full frame, 1x crop Leica S3 FujiFilm GFX, Pentax 645D, Hasselblad X1D Hasselblad H6D 8 mm movie film Super 8 mm movie film 16 mm movie film Super 16 mm movie film Kodak Disc film Minox film 110 film 35 mm movie film Super 35mm movie film APS Panoramic film APS Classic film APS Group, HDTV film 126 film 127 - 40 x 40 mm film 127 - 60 x 40 mm film Half-frame 35 mm film 35 mm film 828 film XPAN film 120 - 6 x 4.5 cm film 120 - 6 x 6 cm film 120 - 6 x 7 cm film 120 - 6 x 9 cm film IMAX film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film

Kinematicdefinition

The equation \((v_f = v_0 + at)\) is used to calculate the final velocity \((v_f)\) of an object in motion, given its initial velocity \((v_0)\), acceleration \((a)\) and the time (\(t\)) elapsed during the motion.

The equation states that the displacement \((\Delta x)\) is equal to half the sum of the initial velocity \((v_0)\) and final velocity \((v_f)\), multiplied by the time \((t)\) taken for the motion.

Units of either feet or meters work, but clicking the  green Ft' In" button  will assume distance is Feet, and will show Dimension results in "Feet and Inches" format. You can click the Green button again to toggle this option off or on. The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

To use kinematic formulas to solve problems, you need to identify the variables that are given and the ones that are unknown. Then, you can use the appropriate formula to solve for the unknown variable.

To polarize is to divide. Something that's been polarized has been split into two sides that are so different, it seems as though they're from opposite ends ...

Once you have identified the variables, choose the right kinematic equation formula to use. Each equation is used to solve for a specific variable. Make sure you choose the equation that allows you to solve for the unknown variable.

Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

The Four distance fields above with green borders (the top Distance, and one in Option 6, and two in Option 9) will always accept distance input in either distance format. The chart at right shows accepted Ft' and In" formats (and always works in these green borders, whether if in Ft" In" mode or Not). Feet or inches can be decimal fractions of feet. Meaning, in these four fields, two values with a space between will be interpreted as feet and inches. Any single value is feet or meters, as you intend as your choice, but any second value is assumed to be added as inches added to feet, regardless of any ' or " on it or not (the ' " are removed, but there must be a space as a field separator). So you can always enter feet either way, just as decimal feet without the inches, such as 8.5 feet, still same format as meters. The combined result is shown with the Magnification result Do use a simple clear method, and I'd suggest that entering fractional 8.25 feet style is always pretty clear. You can verify how the distance result was interpreted, as seen on the Magnification line of the results. The term Native (about sensor dimensions, aspect ratio, or crop factor) is used to mean the actual full size of the original chip area (before cropping to other smaller formats like 16:9 for example). The original size might not be exactly a nominal 3:2 or 4:3 aspect ratio, which is probably very minor, but the calculator accepts any size. Select an Option, and click the Compute button (for all Option numbers). Options 1-5 are four ways to specify sensor size. Options 6 to 8 compute special requirements using the sensor size currently specified in options 1-5. Option 1 - Best accuracy is when entering actual exact sensor dimensions (width and height in mm, from actual camera specifications, for any aspect ratio). If you know them, use them. Option 2 - Was deleted, unneeded following improvements. Aspect Ratio (for options 3 and 4) Options 1 and 5 would already know native Aspect Ratio, but any special features (like 16:9 video format) require more (see Aspect Ratio options). If the red warning triggers, it will be good to double check your settings that Aspect Ratio and Crop Factor do not disagree. Crop Factor is size, and Aspect Ratio is shape, but there are conventions matching them. Generally DSLR are 3:2 in larger sensors (crop factor less than 2, except Four Thirds cameras are 2.7x), and phone and compact cameras are 4:3 in smaller sensors (larger crop factors), but some cameras may provide additional aspect options. One Inch (4:3 2x) and Four Thirds (3:2 2.7x) models both typically provide a menu allowing 1:1, 3:2, 4:3, and 16:9. See the end of the summary of Issues determining Sensor Size for more about embedded formats (video and still photos from same sensor). Option 3 - Second best method to determine sensor size, after 1. Otherwise a known precise crop factor is good, crop factor and sensor diagonal are directly related. Crop factor simply compares sensor diagonal to 35 mm film size, and we know all about 35 mm film size. We can determine the sensor dimensions from the sensor crop factor (if we know the correct Aspect Ratio). Crop factor is another rounded number; all specifications are rounded numbers, but probably close. See more at Determine Crop Factor. Option 4 - This is for when there is no clue about actual sensor size (phones and compacts and camcorders are problems). It computes sensor size using the lens specifications from Equivalent Focal Length on 35 mm film. There is much confusion about the term Equivalent Focal Length. It is Not your lens. Instead, Equivalent focal length means the specification of the hypothetical different lens used on 35 mm film that gives the same Field of View as the different lens that you actually use on your sensor size. What is Equivalent is the size of the Field of View produced by the two combinations of lenses and sensors. The compact camera lens spec normally shows both matching numbers (normally is specified for the ends of the zoom lens range if it zooms). But again, the Focal Length at the calculator's top field is the Real focal length on YOUR camera actually used, and NOT any Equivalent number. The Focal Lengths are NOT equivalent, but it simply means the Fields of View are the same size for those two situations. See this summary of Issues determining Sensor Size for more. Examples of lens specs are shown there. Be sure you understand the methods shown, because improper input simply computes wrong results. Option 5 - You may be able to select one of the general sensor descriptions. Film sizes should be accurate, and the larger sensors with actual WxH dimensions too, but the "1/x inch" sensor numbers are Not fully precise, not actually even related to the digital sensor. See this summary of Issues determining Sensor Size for more. If using Option 5, for example for the 1/2.3" sensor size, 5 does not provide the aspect menu (due to the included film subchoices like 16:9 for movies.) If you want Field of View for 16:9 video, you can use Option 5 to compute sensor size or crop factor, and then use those in Options 1 or 3. The orange  Show All Sensors button in Option 5 will show a summary of all sensors in the Option 5 list, including dimensions, crop factor, aspect ratio and CoC. Options 6-8 still use the sensor size currently described in Options 1-5. The  blue Flip button  (near Option 6) will toggle to swap finding either Focal Length or Distance from the other, with the specified image size in option 6 and 8, to compute either one from the other. This Flip recomputes, but flipping will not show any change unless you change a corresponding number. Angles in Option 7 are not affected by this Flip. Option 6 - Finds focal length and distance combinations to provide a specific Field of View at that distance, for example 2x3 feet FoV for a portrait at subject distance, or 15x10 feet FoV for the background at background distance. The "Flip" allows either specifying distance to find focal length, or vice versa. It uses sensor size currently selected in options 1 to 5. Note that phones that do not zoom cannot change focal length. Option 7 - Angular field is independent of distance, so you can enter a known angular goal, like a relative number to frame the 0.5 degrees of Moon diameter, and just ignore any distance. If a distance is provided, the field dimension there is computed, but it does not influence the angle. If distance is blank, Option 7 will default to distance 10 (so the field math doesn't blow up), but just ignore it then. The calculator still computes FoV angle for the sensor dimension, and field dimensions for the distance. Note that phones that do not zoom cannot change focal length. Option 8 - Magnification. You can assume either feet or meters units in any option if consistent, and if consistent, any choice of units for distance will work for everything there. The other options calculate magnification for BOTH feet or meters. But Option 8 itself needs to know which way is applicable to match it. Any single distance number represents different distances for feet or meters. Dividing the distance in feet by 3.28 converts feet to meters, which will then see the same corresponding magnification number. The magnification number will vary slightly out past a decimal place or two, because the other values likely only have a couple of significant digits. Option 9 - Doubtful of much practical interest, but technically, you could actually measure and enter the actual Field of View Width and Height dimensions at a specified accurate distance (Not at closest lens focus, which changes focal length, but from 10 feet (3 meters) would be much better). Option 9 then operates backwards, to compute the sensor size (and all other numbers there), assuming the focal length and distance are accurate. The math is reversible. Focal lengths are extended longer and less precise up close, so the distance used ought to be at least several feet, or a few meters... or better, twice that. The apparent excessive significant digit precision used here may not have practical meaning, but the purpose is so Option 9 can precisely recompute same sensor size from previous FoV results. There are issues when trying to determine the sensor size of compact or phone cameras, and also with embedded formats (both video and still photo images from the same camera). Video 16:9 may use the assumed full sensor width, or it may not in some cameras. See this summary of Issues determining Sensor Size for more, if any issues. Scaling Field of View Greater focal length magnifies, and smaller sensor size crops. Using different focal lengths on the same sensor size scales the Field of View inversely proportionate. If 2x focal length, the field dimensions are 1/2 size, but the objects therein are 2x size on the sensor. This is the concept of "zooming". If the focal length is 1/2, it suggests a field twice wider, except the sensor size might crop it smaller, the sensor size cannot grow without replacing the camera. However, the Angle of View is Not linear. 2x focal length is NOT half angle. The field size varies with the trigonometry tangent function of the half angle, which is not linear. Wide angles become huge fields, however angles less than 10 degrees can still be considered approximately linear (this is the "small angle approximation" used in math). Using the same focal length on different sensor sizes scales the field frame size proportionately (half of sensor dimensions is 2x crop factor, which is half of field frame dimensions), but the objects therein are the same size. The lens always does what it does, but the sensor size crops it. This is the notion of "cropped sensors". Magnification Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Distance is the total length covered by an object during motion, while displacement is the change in position of the object from its initial to final position.

Incorporate labs into your middle school life science curriculum! ... Contains everything needed to accomplish the 30 different labs except a microscope and some ...

Reproduction Magnification is a related property here. Greater lens magnification reduces Field of View, which calculation becomes inaccurate if magnification exceeds about 0.1 (i.e., if focus is too close, because focal length increases with close distance). However, other than macro lenses, normal lenses typically don't focus any closer. But this FoV calculation is not accurate for macro distances. Macro purposes find it much easier to use Magnification for calculations instead of focal length, that being: Magnification (of object at focus distance) = object image size on sensor / object size in real life. Magnification = sensor size / external field size at focus distance. Magnification at 1:1 macro is 1   (same size image on sensor as the object real size). Magnification of object at Infinity is 0   (infinitesimal in image). The most usable general understanding to compare magnification of focal lengths (for same sensor and same distance) is that the resulting image size is the simple ratio of the two focal lengths. Compared to a 50 mm lens, a 400 mm lens will show an enlarged view 8x the subject size and 1/8 the Field of View (400/50 = 8). This example 1/8 is true of frame dimensional Field of View, or 8x for subject size, however the numeric angle of view number (in degrees) is Not linear with focal lengths. Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Acceleration is the rate at which an object's velocity changes with respect to time. It can be either positive or negative depending on whether an object is speeding up or slowing down. Acceleration can be found by calculating the change in velocity divided by elapsed time and is typically measured in meters per second squared (\(\text{m/s}^2\)). Kinematic equations such as Newton's Second Law are used to calculate acceleration when the force acting on an object and its mass are known.

This calculation requires accurate sensor size and focal length and field distance. Calculators simply MUST be told accurate numbers, else otherwise, the standard saying is "garbage in, garbage out". It will compute with the numbers you enter. That means YOU must know those numbers. All of the problems are from not knowing this accurate data. These values may be very difficult to determine for phones and compact cameras and camcorders, but larger cameras likely show specification values better. Alternately, you can specify an accurate crop factor as a way to compute actual sensor size. Or Option 4 can compute Crop Factor from an accurate lens Equivalent Focal Length specifications (for a 1x sensor). The image's Exif data normally reports focal length. Use the actual real lens focal length with the actual sensor size. If you don't know focal length, the Exif data in the image file probably shows it (zoom lens focal length changes with zoom). The image Exif data may show some what you need to know to obtain some of the required information about your cell phone or compact camera to operate this calculator. Determining this otherwise can be a rather difficult task (especially for video formats), and there are still ifs and buts. If you don't know sensor size, Option 4 can be just the ticket for phones and compacts, but if unsure about what it wants, please see this summary of Issues determining Sensor Size which might help. The biggest risks to FoV accuracy are in not actually knowing the accurate sensor size or accurate focal length, and also of course, your vague guess about the distance likely may not be accurate (but the angle of FOV is not dependent on the distance). DSLR specifications seem easily determined, and their specifications generally specify all the lens and sensor numbers, accurately, even if rounded a bit. But Compact and especially cell phone camera specifications don't bother to tell us much, so you may not find the necessary numbers for this calculator. Some newest phone models do contain two cameras (for wide and telephoto, which use two different sensors — Not necessarily the same sensor size or crop factor). But hints are offered that should determine some usable numbers.

Overall, the formula calculates the net displacement or change in position of the object by subtracting the effect of acceleration from the distance covered by the object in the absence of acceleration.

Finally, plug in the values of the known variables into the equation and solve for the unknown variable. Make sure you use the correct units throughout the problem and round off your answer to the appropriate number of significant figures.

Meaning of magnification in cameras : If the magnification is specified 0.01, that means sensor image is 1/100 of size of the real scene field (and the field at the subjects distance is 100 times larger than the sensor). For example using initial defaults with a 24 mm focal length and Option 8 using Option 1 sensor, specifying sensor size of 36x24 mm, then: The field corresponding to 0.01 size reproduction is 100 times larger, or 24 mm is 94.488 inches Height, which is 7.874 feet Height (100 × 24 mm sensor height), and also computed to occur at 100 × 24 mm focal length = 7.874 feet, which again 24 mm is 94.4488 inches. This is the ratio of 1:100 size. Coincidentally, both sensor height and focal length here are 24 mm, which is not significant, other than they are just numbers. Change Option 8 to use Option 3 sensor of 1.5 crop, 24x16mm sensor size. 100:1 Distance ratio to 24 mm focal length is still at 7.874 feet, but now the sensor Width is 24 mm, so field size of Width now becomes 7.874 feet. The smaller sensor simply "crops" the Field of View smaller, but the magnification remains the same (if focal length and focus distance remain the same). Magnification (for cameras) can be computed in two very standard ways, as was just mentioned. Assuming the same distance, then: Magnification = (Sensor dimension / FoV dimension), horizontal dimension for example. Since macro distance changes focal length drastically from what is marked, macro work uses this dimension method. Magnification = (focal length / field distance) computes same number (similar triangles). Regular lenses only slightly change focal length at distances greater than a few feet (less than magnification 0.1), so focal length can be easier than measuring a distant field dimension. When these dimensions or distances are equal (when image size on sensor is equal to field real life size, or, when field distance is equal to sensor distance), this is 1x magnification, called 1:1 reproduction. But other than at 1:1, camera "magnification" is normally a reduced size on the sensor, normally much less than 1. Magnification of 0.01 means the sensor image is 1/100 size of the real scene Field of View. Magnification of 0.001 means 1/1000 size on sensor. Note: I'm saying "focused distance to sensor" is called "focal length", which it is when focused onto the sensor. The focal length number marked on the lens applies ONLY to focus at infinity. Focal length necessarily becomes a little longer when focused closer. This affects f/stop numbers too, but it only becomes significant in math when magnification grows to approach 0.1 (which generally is slightly closer than most lenses will focus, except macro lenses). Binocular and telescope magnification numbers are different systems than cameras. Binoculars are direct "viewing devices", and their "x power optical magnification" number is relative to the size our naked eye sees at 1x. If the device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, or same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. If the viewing device uses a magnifying eye piece (like binoculars and telescopes use), then their magnification is (main lens focal length / eye piece focal length). So the long focal length main objective lens magnifies, like a camera lens, and the short eyepiece lens magnifies that. But if eyepiece somehow was also the same focal length, that is a magnification of 1, not meaning 1:1, but instead the same size as what the naked eye would see. But cameras don't use this eyepiece to be the same concept. The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

Helios is a compact Time of Flight (ToF) camera with superior depth precision featuring Sony's DepthSense technology. It features four 850 nm VCSEL laser diodes ...

Instantaneous velocity is the velocity of an object at a specific instant in time, while average velocity is the total displacement of the object divided by the total time taken.

The first step in solving any kinematic equation problem is to identify the variables given in the problem. Look for information on displacement, velocity, acceleration, and time. Sometimes, you may need to use other formulas to find these variables before you can start solving the problem.

The magnification result of camera lenses is only seen on the sensor (Not direct viewing), which then that small image must be externally enlarged much more for viewing. If no eyepiece lens is used (if telescope is attached like a camera lens, called prime focus photography), then the normal camera Magnification = focal length / subject distance applies. Our Moon is 3474 km diameter, and its appearance here on Earth is only near 0.5 degrees size. Then 10x binoculars will show it enlarged to apparent 5 degree size. But the size of the moon is only a few mm on our camera sensor, so the camera math sees that as an extreme size reduction, and not likely a meaningful number. It becomes meaningful at macro distances like 1:1 magnification. Some uses in astronomy in the past attempted to compare cameras and telescopes as if a 50 mm lens gives 1x magnification (so a 2000 mm telescope directly attached as prime focus lens might be said to give 2000/50 = 40x, 40 times larger than a 50 mm lens sees). That 1x of 50 mm is a confusion factor; it is simply relative to a 50 mm lens instead of to our naked eye or to any other lens. Back in the day, a 50 mm lens was considered the "normal lens" if on a 35 mm film body, which used to be very popular. However in a different sensor size situation today, 50 mm and its Field of View may not have meaning to your situation. Nevertheless, in this 2000 mm case, 2000 / (your comparison lens focal length) would still give a meaningful comparison size number of those two lenses. That's all the 50 mm comparison tries to do, but many fewer people use a 50 mm camera lens today. Compact and cell phone camera lenses are normally about maybe 4 mm (unless zoomed). Use your own lenses focal length number there. But cameras are a "reproduction device", and the magnification number is relative to the actual real life size of the field being reproduced. Maybe except for the largest film, it will be enlarged more when we view it. So obviously, on the sensor, sensor dimension / FoV dimension (or likewise, focal length / subject distance) is the actual magnification, normally a size reduction. For example, reproduction size of 1/100 is 0.01x or 1:100... on the sensor. In contrast, the DSLR viewfinder magnification specification has an eyepiece, and is compared to the eye's view (which is called 1x), regardless of the camera lens attached (it's only about how well we see the viewfinder image of the image on the sensor). But otherwise, the magnification of that lens image is instead compared to the reproduction size of the distant Field of View (affected by focal length and distance). Lens magnification is Not affected by sensor size, the lens simply does what it does, and the sensor captures what it is able to see. A mountable macro lens that does 1:1 simply does 1:1 size on any size sensor, but a larger sensor sees a larger field. Field size is affected by sensor size, and Field of View may be cropped proportionally smaller by a smaller sensor, but an object size in the lens image is unchanged (if focal length and distance are unchanged). Magnification is f/d, and is directly proportional to focal length or inversely to distance. 2x focal length is 2x more magnification of field size. 2x distance is 1/2 the magnification of field size. Therefore the combination of 2x focal length AND 2x distance together remain the same magnification and same field size. See the Depth of Field page for more about using that principle. Actually knowing the accurate precise sensor size and distance is the key to Field of View accuracy (but approximations may be useful too). Next page is a chart of angular Field of View (degrees) for many lens focal lengths and a few popular sensors. And there is also a FoV Math section for FoV. Menu of the other Photo and Flash pages here

The term \(v_0t\) represents the displacement that the object would have covered during the time \(t\), if it had moved at a constant velocity \(v_0\). The second term \(\frac{1}{2}at^2\) represents the additional displacement that the object covers due to its acceleration.