Lens Field of View by Focal and Sensor

Angle of view from focal length and sensor

The angle of view (AoV) comes from AoV = 2 · arctan(d / (2·f)), where d is whichever sensor dimension you care about (width, height or diagonal) in millimetres and f is the focal length. On a full-frame sensor that's 36 mm wide, a 50 mm normal lens covers about 39.6° horizontally, a 24 mm wide opens up to 73.7°, and a 200 mm telephoto squeezes down to just 10.3°. Move to APS-C and the 1.5× crop factor narrows everything, so a 50 mm frames like a 75 mm equivalent.

Applications

Wide lenses for landscape work, telephoto for sports and wildlife, a vlogger rig built around 24 mm full-frame equivalent, working out surveillance camera coverage, and storyboarding for cinematography.

FAQ

Why does the same lens look tighter on a smaller sensor? Because d gets smaller. APS-C uses roughly 23.6 mm of width against 36 mm on full-frame, and that narrower dimension gives you a narrower AoV.

Horizontal, vertical or diagonal AoV? Horizontal tells you how wide the frame is. Vertical is what decides how much sky or ceiling fits. Diagonal is the biggest of the three, and it's usually the figure printed in lens specs.

Does it work for fisheye lenses? Only roughly. Fisheye optics rely on non-rectilinear projections (equisolid, equidistant), so the 2·arctan formula comes out low compared to their actual coverage.