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Looking at this online lens calculator, it seems that the 42mm on my Canon has a FOV of 46 degrees, and that the Sony would have a Full Frame equivalent of 18mm.

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And, yeah, a horizontal field of view of 89° does indeed translate to about 18mm in full frame. 18.32mm, to be more precise, although that is probably more precision than is useful. (Since 35mm film is 36mm across, half of the width is 18mm, which means an 18mm lens gives perfect even 90° horizontal field of view.)

So, my question is, can I trust that lens calculator? I really don't want to spend hundreds of dollars only to find out it doesn't work.

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An 18mm focal length does indeed yield an horizontal Field of View (FoV) of 89°- if it is projecting onto a FF sized 36 x 24mm sensor.

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I'm trying to shoot wider than the 42mm that my Canon 5dMkII shoots at. Working with the manufacturer, he suggests that I switch to the Sony NEX system, which is the widest system he sells. That has a field of view of 89 degrees.

Focal length from field of view is really simple and covered in my answer to What is “angle of view” in photography?. The formula for field of view in degrees is 2 × arctan( half sensor size ÷ focal length). Because this formula is so simple, I see no reason for the calculator you're using to be wrong (and it indeed seems to match my validation).

Zone sieve/plate does not use a glass lens, but rather a pattern of dots or rings which diffracts the light. You cannot change the focal length of the zone, it is fixed and a characteristic of the physical dimensions of the camera, basically, the distance from the zone to the sensor is the focal length.

I'm working with zone sieve and zone plate photography. Zone sieve/plate is similar to pinhole photography but it can give a softer, dreamier, look. This is a zone sieve photo I've taken:

In the case of the Sony NEX, the smaller APS-C sized sensor (23.4 x 15.6mm) means a plate placed at an 18mm focal length (the E mount flange focal distance) will yield an FoV of around 67°. The new Sony α7 and α7R are Sony E mount cameras that do place FF sensors at an 18mm flange focal distance, but are also considerably more expensive than the NEX series of Sony E mount cameras.

If, on the other hand, the plate from your vendor would sit at 12mm in front of the sensor on the NEX (a possibility since there is no mirror to cause clearance issues), then it would yield an 89° FoV with the NEX. The vendor linked in your comments to your question indicates on this page the plates designed for the Sony E mount system sit at 13mm from the sensor, so that will yield an FoV of about 85° with an NEX sized sensor. Scroll past the other Sony mount systems all the way down to the bottom of the page to see the specs for the plates for the Sony E mount system.