# How do I calculate equivalent focal length from field of view?

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:

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 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.

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.

Now, 18mm on a Full Frame camera is a pretty sweet spot for landscape photography.

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.

• Please provide a link to this product. What is the diameter of your current plate? By the way, this effect can be easily reproduced with a convolution filter in Photoshop, so you could just shoot away with any lens, and add the effect in postprocessing... Commented Dec 30, 2013 at 15:20
• @TFuto "This effect can be easily reproduced" really misses the point. Commented Dec 30, 2013 at 15:50
• Also, I think you underestimate the effort required and are probably mislead by the low-resolution sample given. You may be able to approximate the look but a single photo simply won't have all of the data needed to really reproduce it. You would need a light field array.... Commented Dec 30, 2013 at 15:52
• skinkpinhole.com is the vendor. Commented Dec 30, 2013 at 15:52
• and don't forget the almost infinite depth of field that shooting at f50-f100 gives you... Commented Dec 30, 2013 at 15:55

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).

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.)

• Since the flange focal distance of the Sony E-mount is 18mm, I have a slight suspicion that the vendor is actually calculating from that and not taking the sensor size into account, and that the real field of view is 67° (or about 27mm in full-frame equivalency, just as with the normal crop factor). I think I'd double-check.... Commented Dec 30, 2013 at 21:45
• I've not handled the product yet but I spoke with the vendor about a year ago and suggested that they could actually inset the plates on mirrorless cameras, maybe he did! Commented Dec 31, 2013 at 11:58

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.

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.

Illustrations were generated with Aaron Isotton's Lens Angle Calculator.