How do I calculate full-frame equivalent focal length from field of view?
Asked 12/30/2013
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2 answers
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I’m using a zone sieve/zone plate camera setup, where the image-forming element has a fixed distance to the sensor, so the effective focal length is fixed by the camera design. I currently get about a 42mm equivalent field of view on a Canon 5D Mark II and want something wider for landscapes.
A manufacturer suggested switching to a Sony E-mount/NEX-style system and says the setup would give an 89° field of view. An online calculator suggests that 89° horizontal field of view is roughly equivalent to an 18mm lens on full frame.
Is that calculation correct, and what do I need to watch out for when comparing field of view and equivalent focal length across different sensor sizes?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
12y ago
2 Answers
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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.)
Originally by user1943. Source · Licensed CC BY-SA 4.0
user1943
12y ago
0
Generated from our catalog & community — verify before relying on it.
Yes — the calculator is likely correct, but only if you’re comparing the same sensor dimension.
Field of view is calculated as: 2 × arctan((half the sensor dimension) ÷ focal length)
For full frame, the sensor width is 36mm, so an 18mm lens gives almost exactly a 90° horizontal field of view. That means 89° horizontal FoV is indeed about an 18mm full-frame equivalent.
The important catch is sensor size. A given focal length produces a narrower field of view on a smaller sensor. So if a setup is mounted on Sony APS-C/NEX, you only get 89° if the zone plate is positioned at the appropriate distance for that smaller sensor. If the imaging distance were 18mm on APS-C, the horizontal FoV would be much narrower (around 67°), not 89°.
So: trust the math, but verify what the 89° refers to — horizontal, vertical, or diagonal — and on which sensor size. The real question is not just the mount, but the actual sensor dimensions and the distance from the zone plate/sieve to the sensor.
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