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# How to calculate the horizontal angle of view

edited April 2013
Up to today, I had always used the multiple of 0.83 times the diagonal field of view to attempt to know what the horizontal field of view was. My calculations were based upon the Pythagorium theorem, which is a about the sum of squares of the two sides is equal to the square of the hypotenuse.

Wrong...this is not the way to do it. It involves a calculation using tangents, angles, etc. This came to light when I was looking at the Zeiss Distagon T* 2,8/15 and noted the diagonal FOV is 110°, the horizontal FOV is 100°, and the vertical FOV is 76°. And, these are not the numbers I got using the method I had been using.

I emailed Zeiss. I think I have gained such respect for the customer service I may have to get this lens. Within a few hours, I had a very nice explanation of how this is calculated, along with nice diagrams. Unfortunately I cannot figure out how to draw the image, but the formula is

tan (alpha/2) =18mm/15mm and alpha comes to 100.4° for the full frame 35mm sensor. Note, alpha is the angle, 18mm is half of the horizontal plane, and 15mm is the focal length of the lens. So, if anyone wants to do this calculation, which I like as Nikon does not seem to publish the horizontal FOV, the easy way is via a link and I am placing this here;
http://www.isotton.com/misc/lens-angle-calculator/

I think some of us may find this of interest, especially for the architectural and landscape shooters. And, Zeiss has gained so much respect from me...well...
Msmoto, mod

• Msmoto, this topic is a little over my head and I don't understand when I would need to know this. Could you explain to me the situations where I would need to apply this.

Thanks
• If you look at Nikon lens data, the FOV is in degrees. But, this is the diagonal FOV. Basically, if one wants to know what lens will show four sides of a room from a corner, then one must calculate the horizontal FOV. Or if one has the desire to shoot a very wide landscape in a single shot...same thing. Zeiss provides this, Nikon as far as I have found does not give the horizontal nor vertical FOV in the data generally provided.

The comparison of wide lenses can be assisted by understanding this. Also, very long lenses give a narrow angle and it can be useful to know what that horizontal FOV is so as to determine if a subject will fit into the frame.

This might be more for those who are a bit on the geeky side, but I supplied this because I had not been calculating the FOV correctly.
Msmoto, mod
• @Msmoto, you may recall this discussion from a few months back:
http://forum.nikonrumors.com/discussion/comment/17302#Comment_17302
Anyway, the web site that I mention there also has a bunch of different DOF and FOV calcs. The "Angular Field of View Calculator" agrees with your calculations (although the vertical is off by 1deg).
• ok, I understand now. I have an app that also calculates this and now see what you are talking about.
• edited April 2013
Similar discussion, but the link to the calculator is so good, very easy to figure the angle. Or put in the angle it tells the lens focal length.
Post edited by Msmoto on
Msmoto, mod