How can I calculate vertical field of view from horizontal field of view?

Question

I have an Axis M1011 (specs available here), which I need to find the vertical field of view. The online specifications tell me the horizontal field of view is 47 degrees, and the image size is 640x480. Does this mean that the vertical field of view will be 32.25 degrees?

Asked by Joel

Answer

The formula for this calculation is:

a = 2 arctan(d/2f)

Where 'a' is the angle, 'd' is the size of the sensor in the direction of interest, and 'f' is the focal length. The real angle of view of this combination is actually much better than what you get but, because it's video (which is technically off topic here, but the basic question isn't), you're lopping off some info.

The camera's sensor is 6.35mm (1/4 inch according to doc), so if it holds to standard 3:2, then the vertical is about 4.23mm. So...

• True horizontal is: 71.63 degrees
• True vertical is: 51.35 degrees

If I do a little bit of math, it would appear that the sensor is about 167 pixels per mm, so the vertical is using about 2.87mm of the sensor. That leads to the formula returning: 36.13 degrees or thereabouts, call it probably 36. How did I arrive at the 167? Well, the formula to yield an angle of 47 degrees would imply the horizontal is using about 3.83mm of the sensor and if there are 640 pixels, the math works out to about 167 pixels per mm.

Mind you, without real specs on the sensor, this is all approximation. However, the formula I gave you is correct. :)

Answered by John Cavan

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