Field of View & Focal Length
Horizontal, vertical and diagonal angle of view for a lens and sensor, the scene it covers at a distance, or the focal length for an angle or frame width.
The three angles of view, the width and height of scene covered at your subject distance, the full-frame equivalent — or, working backwards, the focal length that gives the angle or the frame width you want.
Example: A 50 mm lens on full frame sees 39.6° × 27.0° (46.8° diagonal) and at 10 m takes in 7.2 × 4.8 m; a 90° view across on APS-C needs 11.75 mm.
Sensor over
focal length.
How the angle of view comes from the sensor and the lens, how coverage at a distance scales, how to work back to a focal length, and what the figures assume.
The angle
A lens focused at infinity projects the scene onto the sensor; the angle it takes in across a sensor dimension d is 2·atan(d ÷ 2f). Width, height and diagonal each give their own angle, and a lens’s “angle of view” on a spec sheet is usually the diagonal one.
Coverage at a distance
Similar triangles: at a subject distance D the frame covers d × D ÷ f of the scene in each direction. Working backwards, a wanted frame width gives the focal length f = d × D ÷ width, and a wanted angle θ gives f = d ÷ (2·tan(θ/2)).
Sensor sizes
The presets are nominal sensor dimensions as commonly published; real sensors differ by tenths of a millimetre and some cameras crop in video modes, so enter your camera’s own figures when it matters. The full-frame equivalent is the focal length times the crop factor.
What the number does not settle
Infinity focus and rectilinear projection: close up, most lenses change their effective focal length (focus breathing), and fisheye lenses follow a different projection. Inputs stay in your browser; the same anonymous usage counts as the rest of the site apply.