My old engineering studies made me revisit this question. The reason it is not simple comes down to standardized, normally to 35 mm cameras, focal lengths. Below is a page that shows the formula, and, it does relate directly to the sensor size. But, as others have shown on here, different manufacturers, and even fixed versus varifocus cameras of the same model are different. Hence the recommendations of using the manufacturers stated angle of view.
Anyways, for those so inclined, here is a link to an explanation and foumula, complete with arctan. This calculation is also the basis of the DORI calcs and formula used in the
wiki that was discussed on here a few days ago in relation to how far can you identify someone. .
Field of view is a lens characteristic that is directly related to the focal length of your lens and determines how much you can see with a lens.
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