Lens Angle of View Calculator

Enter the focal length and sensor size to find the lens angle of view.

Result

39.60°
26.99°
46.79°

How it is calculated

Each angle follows AOV = 2 × arctan(d / (2 × f)) in degrees, where f is the focal length in mm and d is the sensor dimension in mm. The tool runs it three times: with the sensor width for the horizontal angle, the sensor height for the vertical angle, and the diagonal √(width² + height²) for the diagonal angle. All three inputs must be in millimetres and greater than zero, otherwise there is no result. The sensor size you type is what matters: the tool does not know your camera, so a crop sensor needs its own width and height. The focal length is used as marked on the lens, and it is assumed to be focused at infinity, so close-focus lenses that change their effective focal length will frame slightly differently.

Worked example

A 50 mm lens on a full-frame sensor of 36 × 24 mm. Horizontal: 2 × arctan(36 / 100) = 2 × arctan(0.36), which gives 39.60°. Vertical: 2 × arctan(24 / 100) gives 26.99°. The diagonal of the sensor is √(1296 + 576) ≈ 43.27 mm, so 2 × arctan(43.27 / 100) gives 46.79°. The tool shows these as 39.60°, 26.99° and 46.79°. The same lens on a 23.5 × 15.6 mm APS-C sensor would give a narrower 26.45° horizontally.

Try this example →

Common mistakes

  • Typing the sensor size in inches or in the "1/2.3-inch" style of the spec sheet. The fields take real width and height in millimetres.
  • Swapping width and height. The wider side of the sensor gives the horizontal angle, so reversed values mix up the two results.
  • Quoting the diagonal angle as the lens angle. Spec sheets usually list the diagonal, and the horizontal angle of the same lens is noticeably smaller.
  • Entering the 35 mm equivalent focal length together with the real sensor size, which counts the crop factor twice. Use the actual focal length with the actual sensor.
  • Expecting a zoom lens to have one answer. Calculate it separately at each end of the zoom range.

About this calculator

The angle of view of a lens is the extent of a scene captured on the sensor, calculated as AOV = 2 × arctan(d / (2f)), where d is the sensor dimension (width, height, or diagonal) and f is the focal length. A shorter focal length or larger sensor widens the angle of view, while a longer focal length or smaller sensor narrows it — which is why the same 50mm lens frames dramatically differently on a full-frame body versus an APS-C or Micro Four Thirds camera.

Because sensor size varies so much between formats, angle of view (not focal length alone) is what actually determines how “wide” or “telephoto” a shot looks. Photographers, cinematographers, and lens manufacturers use this calculation to compare lenses across different camera systems, choose the right focal length for architecture, portraiture, or landscape work, and convert a lens's field of view when switching between full-frame and crop-sensor bodies.

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