Angle of View Calculator
The angle of view determines how much of a scene a lens captures. It depends on the focal length of the lens and the size of the sensor. Shorter focal lengths and larger sensors give wider angles of view; longer focal lengths and smaller sensors produce narrower fields. This calculator applies the exact optical formula: AoV = 2 x arctan(sensor dimension / (2 x focal length)), giving horizontal, vertical, and diagonal angles of view for any lens and sensor combination.
Angle of view formula
AoV (deg) = 2 x arctan(sensor_dimension / (2 x focal_length))
Diagonal = 2 x arctan(sqrt(w^2 + h^2) / (2 x focal_length))
Example: 50 mm lens on a 36 x 24 mm full-frame sensor. Horizontal: 2 x arctan(36/100) = 39.60 deg. Vertical: 2 x arctan(24/100) = 27.00 deg. Diagonal (sensor diag = 43.27 mm): 2 x arctan(43.27/100) = 46.79 deg.
Sensor size quick reference (mm)
- Full-frame (35mm): 36 x 24 mm, diagonal 43.27 mm
- APS-C Canon: 22.3 x 14.9 mm, diagonal 26.82 mm
- APS-C Nikon/Sony/Fuji: 23.5 x 15.6 mm, diagonal 28.22 mm
- Micro Four Thirds: 17.3 x 13.0 mm, diagonal 21.64 mm
- 1-inch: 13.2 x 8.8 mm, diagonal 15.86 mm
Angle of view calculator: frequently asked questions
What is the angle of view in photography?
The angle of view (AoV) is the angular extent of the scene captured by a camera, measured in degrees. A wide angle of view captures a broad scene; a narrow angle captures a small area from far away. It depends on both the focal length and the sensor size.
How is angle of view calculated?
AoV = 2 x arctan(sensor dimension / (2 x focal length)). For horizontal AoV, use sensor width. For vertical, use sensor height. For diagonal, use the sensor diagonal. A 50 mm lens on a 36 mm wide full-frame sensor has a horizontal AoV = 2 x arctan(36 / 100) = 2 x 19.8 = 39.6 degrees.
Why does sensor size affect angle of view?
A larger sensor captures a wider portion of the lens image circle. Given the same focal length, a larger sensor records a wider field of view. A 50 mm lens on a full-frame sensor has a 39.6-degree horizontal AoV, but on a 1.5x APS-C sensor it captures only 26.7 degrees horizontally.
What is the angle of view for a 50 mm full-frame lens?
Full-frame sensor (36 x 24 mm). Horizontal AoV = 2 x arctan(36 / 100) = 39.6 degrees. Vertical AoV = 2 x arctan(24 / 100) = 27.0 degrees. Diagonal (43.27 mm sensor): 2 x arctan(43.27 / 100) = 46.8 degrees.
What focal length gives a 90-degree angle of view?
For a 90-degree horizontal AoV on a 36 mm wide full-frame sensor: 90 = 2 x arctan(36/(2f)), so tan(45) = 36/(2f), 1 = 36/(2f), 2f = 36, f = 18 mm. An 18 mm lens on a full-frame sensor has approximately a 90-degree horizontal angle of view.
Official sources
- ISO 10110: Optics and photonics, Preparation of drawings for optical elements. ISO.org.
- NIST: Optical measurements and standards. NIST.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.