angular field of view (FOV) or angle of view (AOV)

introduction

angular field of view is the viewable scene through your system measured as an angle
human cone of visual attention is ~55deg which equates to a 43mm focal length lens on a 35mm full frame camera hence lenses with focal lengths in that vicinity are regarded as “standard lenses”

angle of view in radians = 2 x arctan (d/2f) where d = size of dimension of sensor in mm and f = effective actual focal length in mm
for telephoto lenses, this approximates to angle of view in degrees = (180/pi) * (d/f)
effective focal length:
- for most photography, this is the actual focal length as stated for the lens
- for macrophotography, the effective focal length = actual focal length x (1+magnification factor), such that for a 1:2 macro, the magnification factor is 1.5
- for telescopes, effective focal length depends upon whether other elements are used and how they are used such as eyepieces and Barlow lenses
as an example of subject size, apparent angle of the moon and sun is approx. 0.5 deg

effective focal length	horizontal fov	vertical fov	diagonal fov
50mm	39.6	27.0	46.8
100mm	19.8	13.5	23.4
200mm	9.9	6.75	11.7
300mm	6.6	4.5	7.8
400mm	4.95	3.38	5.85
500mm	3.96	2.7	4.48
1000mm	1.98	1.35	2.34
2000mm	1	0.68	1.17
5000mm	0.4	0.27	0.45

sensor size is 17.3 x 13.0mm and a diagonal of 21.63mm = half the diagonal size of a 35mm sensor hence the 2x “crop factor”

effective focal length	equivalent focal length in 35mm system	horizontal fov	vertical fov	diagonal fov
45mm	90mm	22	16.5	27.5
50mm	100mm	19.8	14.88	24.78
75mm	150mm	14.85	11.16	18.59
100mm	200mm	9.9	7.44	12.39
135mm	270mm	7.3	5.5	9.2