If you want maximum information from the background, showing both subject and environment, go wide.  The depth of field will be greater, and more individual elements will be visible, and identifiable even if blurred.  If you want minimum information, all the attention on the subject, go long.  Not only will the objects be blurrier, but they will be relatively larger and fewer, and likely more abstract and less distracting.

Field of viewhuman eye

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If you look into the formula used by dof calculators you see that magnification is squared but aperture isn't, meaning magnification has more impact on depth of field. Magnification is estimated in calculators to be focal length divided by subject distance, so you see how much more impact  change of focal length has.

To fill the frame with a subject at a shorter focal length, you have to decrease the subject distance...but if you increase the subject distance, and zoom in to get an equivalent FoV...DoF decreases....

Let's suppose I want to take a picture of a flower and fill the frame. I want the whole flower in focus, but everything else out of focus...w/o stacking.

Shallowdepth of field

Fill the frame with every lens you have. Taking macros means f11-f18 and everything in the frame will be in focus regardless what lens you choose.

Depth of fieldphotography

The differences in your images can be pretty remarkable - especially as you try this with different focal lengths.  You can vary the exercise by using a zoom lens.  Take a series with the widest focal length, and another series with the longest focal length.

I'm trying to get my head around how to balance focal length, subject distance, aperture, magnification and depth of field for an equivalent field of view.

Depth of fieldmicroscope

This exercise will allow you to see how close you can get and what a subject looks like when you are really close.  It will also show you what happens to DOF, field of view, composition, and the relative importance of your subject as you move back or change orientation.

Even at f/16 the depth of field is incredibly narrow at macro distances.  30cm away from the depth of field is like...half a cm according to Photopills.

Take your favorite every day lens, and photograph a subject by getting as close to the subject as the lens allows.  Then with the same focal length and subject, make an image after moving back two feet, and then another image after moving back 5 feet and then 10 feet.  With each image, try to make the best composition possible of the scene and your original subject.  Your subject can be anything - a flower, a pet, a person, or an object.  Your photo can be inside or outside.  Just make the best image you can

There is no free lunch. If you want to defy the laws of physics, you’ll have to do focus stacking, but running back and forth with a zoom lens will do nothing for DoF.

Depth of field vs field of viewcamera

Perspective on the other hand is only related to camera to subject distance. So if you stay in one place and change focal length you don't change perspective, but if you back up you change perspective meaning something blurry behind the subject can appear bigger relative to the subject than it would if you were closer. Point being its easy to mistake a bigger blur spot for less DOF.

Depth of fieldphotography examples

Although it's true that decreasing distance decreases DOF, and thus the shorter focal length will result in a decrease, it's also true that the longer focal length will have less depth of field to begin with, and and its decrease beats out the distance decrease.  Though they cancel out to a certain degree, the longer focal length decreases DOF more than the shorter distance.  But more importantly for some things, it also changes the actual content of the background, a consequence that cannot be changed by changing aperture.

Depth of fieldexamples

Fixing FoV also fixes the ratio of the focal length to the camera-subject distance - if you step back, you need a longer focal length to keep the framing of your subject constant.

You can't take a picture from farther away and then crop expecting to keep the better depth of field. The reason is when you resize the images for the subject to be the same you also alter the depth of field.

If you have a zoom lens, here's a quick version of the above that you can do to determine just what changes in the out of focus areas as focal length changes.

Although it's true that decreasing distance decreases DOF, and thus the shorter focal length will result in a decrease, it's also true that the longer focal length will have less depth of field to begin with, and and its decrease beats out the distance decrease.  Though they cancel out to a certain degree, the longer focal length decreases DOF more than the shorter distance.  But more importantly for some things, it also changes the actual content of the background, a consequence that cannot be changed by changing aperture.

Fill the frame with every lens you have. Taking macros means f11-f18 and everything in the frame will be in focus regardless what lens you choose.

I think I ran out of edit time, but here, for example, is a very quick and dirty comparison, two shots made at the same aperture (shadow from flash in one), first at 24 mm, and then at 80 on a DX camera.  Neither of these lengths is radical enough to cause odd distortion of the subject, but note not only the difference in background blur, but in the actual content.

I'm trying to get my head around how to balance focal length, subject distance, aperture, magnification and depth of field for an equivalent field of view.

Now the cool part. If this is portraiture or close up or wildlife photography (basically anything but landscape when you shoot close to the hyperfocal distance), under fixed framing, the depth of field (DoF) depends only on the f-stop. You cannot change it in any other way. A head shot at f/4 will have the same DoF whether it was taken using a 50 mm lens from a meter away or using a 200 mm lens from 4 meters away. The perspective will change, the appearance of the background will change but the DoF will stay the same.

Depth of field vs field of viewphotography

Do I get closer with a shorter focal length or stay further away and zoom in, but stop down the aperture? Or shorter and crop? Shut up and stack? Take up stamp collecting instead?

For my experiment I just put an object on a table, with a shelf full of assorted stuff a few feet behind the object.  Now take pictures of the object using different focal lengths of the same lens, at the same aperture (make sure it's the same on a variable-aperture zoom), each time with the object the same size in the frame, and if possible at the same level.  You vary only the distance and focal length to make the object the same size in the frame. You will see that not only will the depth of field be different, but the perspective between the object and the background will be different as well. This latter bit becomes really important for composition at times.