- If Df is the diagonal field of view and Ha:Va is the horizontal to vertical aspect ratio, we can find the corresponding diagonal size in the same units as the aspect ratio:
Da = sqrt(Ha*Ha + Va*Va)
- The screen height and width are proportional to the tangent of the half angle. We use this to convert between field-of-view space and aspect-ratio space:
Da = tan(Df/2) and Df = atan(Da) * 2
- If the tangent and arctangent functions operate in degrees, we get:
Hf = atan( tan(Df/2) * (Ha/Da) ) * 2
- Here the tan() function converts from FOV to aspect-ratio space, the ratio is scaled in that space and then converted back into FOV space.
