Lens Field of View Calculator
A lens projects an image circle onto the camera sensor, and the angle of view is how much of the scene that combination captures. It is set by two things: the focal length and the sensor dimensions. This calculator returns the horizontal, vertical, and diagonal angle of view in degrees from your focal length and sensor width and height. Use it to compare lenses, plan how much of a scene will fit, or check how a lens behaves on a different sensor format.
Angle of view formula
AOV = 2 * atan( d / (2 * f) )
Horizontal: d = sensor width
Vertical: d = sensor height
Diagonal: d = sqrt(width^2 + height^2)
f is the focal length and d is the relevant sensor dimension. The result is in radians from atan, so it is multiplied by 180 / pi to convert to degrees.
Worked example
A 50 mm lens on a full-frame sensor (36 by 24 mm): horizontal AOV = 2 * atan(36 / (2 * 50)) = 2 * atan(0.36) = 39.60 degrees. Vertical = 2 * atan(24 / 100) = 26.99 degrees. Diagonal uses sqrt(36^2 + 24^2) = 43.27 mm, giving 46.79 degrees. This matches the familiar normal-lens field of view.
Field of view: frequently asked questions
What is angle of view?
Angle of view is the angular extent of the scene a lens captures, measured in degrees. It depends on the focal length and the size of the recording sensor: a shorter focal length or a larger sensor gives a wider angle of view.
How is angle of view calculated?
The angle of view in one dimension is 2 times the arctangent of the sensor dimension divided by twice the focal length: AOV = 2 * atan(d / (2f)). Computing this for the sensor width, height, and diagonal gives the horizontal, vertical, and diagonal angles.
Why does a full-frame lens look wider than the same lens on a crop sensor?
A smaller sensor captures a smaller slice of the image circle, so for the same focal length the angle of view narrows. That is why a 50 mm lens behaves like a normal lens on full frame but like a short telephoto on a smaller APS-C sensor.
Sources
- NIST: Office of Weights and Measures (length and angle units).
- The angle-of-view relation AOV = 2 atan(d / 2f) is standard thin-lens optical geometry.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.