View Full Version : calculating image circle from AOF and Focal length

15-Jun-2007, 07:42
Someone somewhere posted a spreadsheet datum on calculating a lens' image circle size by plugging in focal length and angle of field. It's on my desktop at home, but I'm on the road. Would someone please post this again (or point me to the old thread, I did a search but didn't find it) for a poor geometrically challenged fool?:o

Or, the answer I'm really trying to find out is does a Goerz Dagor Series III 6.3 210mm lens even remotely cover 8x10?:confused:

Thanks much!

Ernest Purdum
15-Jun-2007, 08:00
Not being a mathematical type, I like to do it by measurement on paper. Draw a horizontal line near the bottom of a sheet of paper turned sideways. On this line, measure and mark your focal length. Now use your kid's drawing compass to make a diagonal line at one half of the lenses angle from the left hand focal length point. From the right hand focal length point erect a vertical line up to the diagonal line. Measure the vertical line, double it, and you have your image circle diameter.

15-Jun-2007, 08:03
2xthe focal lengthX [[1/2 the angle of coverage]tan]

You'll need a coverage angle of 75 degrees or higher. Higher better.

Leonard Evens
15-Jun-2007, 08:18
What you need to do is take the tangent of half the angle of field and mutliply is by twice the focal length.

If you are using a computer, it undoubtedly has a calculator accesory which can be put in scientific mode. You should be able to apply the above rule. Usually the calculator is set by default to take angles in degrees, which is how the AOF will be specified.

If you want to do it with a spread sheet, you have to enter something like


where F is the focal length and AOF is the angle of field. Unfortunately, the AOF may need to be in radians. If you have it in degrees, then modify the above formula to


This gives the diagonal of the image circle when focused at infinity. If you are closer, use the bellows extension instead of the focal length.

There is one caveat. The above calculations apply if by "angle of field" you mean the angle subtended by the full usable image circle. It could on the other hand mean just that part subtended by the diagonal of the format, usually called angle of view. In the latter case, you will just recover the diagonal of the format.

I will be happy to calculate it for you if you give me the AOF as well as the focal length.

15-Jun-2007, 08:29
Thanks to all for such fast responses. I think the answer for the Dagor is 'almost, at infinity'.

Leonard, the lens in question is one that I haven't bought yet, but that I'm considering. It's a 210mm length and I believe from the limited amount of info I could find on it that the angle is around 70 degrees. Thanks for going through the trouble for me.

15-Jun-2007, 08:33
I get 294mm image circle at infinity; is my math right? :o Part of the problem is that I can find very little information on this lens mentioned above, so the angle is in question. I've heard 70 degrees mentioned, but also 90 degrees for the wide angle version of the lens. This one is a Series III so I believe that that would not be the wide angle version.

Thanks again to all for the formula!

Dan Fromm
15-Jun-2007, 10:17
f/6.3 Dagor? Don't you mean f/6.8?

Coverage claims for that class of lens range from 70 degrees at infinity to 85 degrees at infinity. Coverage is, as always, in the eye of the beholder. My guru on one member of the f/6.8 Dagor family insists that 70 degrees at f/22 is all a reasonably demanding user will find.

Per Dr. Evens formula a 70 degree 210 mm lens won't quite cover 8x10, its circle is the 294 mm you already got. Now try the lens out at f/22 or smaller. You might be willing to live with what it gives you.

15-Jun-2007, 10:29
Thanks Dan, yes, I meant 6.8. I'm thinking that it may be a nice lens to do some portrait work and florals where I'd have a good amount of bellows extension as well, so it would probably be fine for 8x10 in that regard.

Thanks again all!

Jack Flesher
15-Jun-2007, 11:27
Here is a thread where I give the forumula for excel and others posted some other methods and a neat web link if you are interested: http://www.largeformatphotography.info/forum/showthread.php?t=25337&highlight=angle+coverage