Apertia · Library
Why do horizontal and vertical field angles differ on the same sensor?
Work out horizontal, vertical and diagonal angles with 2 × atan(size ÷ 2f) and see why a 24 mm lens covers 73.74° across but only 53.13° up a full-frame sensor.
One formula, three sensor dimensions
Each field angle in this model comes from the same rectilinear relation: angle = 2 × atan(sensor dimension ÷ (2 × focal length)). Apertia's onboarding shows the horizontal angle for the lens you pick, using the long side of the selected sensor preset. Feeding the short side into the same formula gives the vertical angle, and the diagonal of the rectangle gives the diagonal angle that lens makers usually print.
Because the preset widths and heights are fixed numbers, the gap between the angles depends only on the sensor's shape and the focal length. A 3:2 full-frame sensor (36 × 24 mm) always produces a narrower vertical angle than horizontal one, and turning the camera to portrait simply swaps which of the two describes the scene's width.
Worked example
For a 36 × 24 mm sensor and a 50 mm focal length, the ideal angles are about 39.598° horizontally and 26.991° vertically. The same number should not be used for both dimensions.
- Horizontal angle (degrees)
- 39.597753
- Vertical angle (degrees)
- 26.991467
Calculate the angle that limits your subject
- Pick the sensor preset that matches your recording area and note its width and height in millimetres.
- Use the real focal length printed on the lens, not a full-frame equivalent label.
- Decide whether the subject is limited by its width or its height in the frame you intend to shoot.
- Compute 2 × atan(dimension ÷ 2f) for that side and convert radians to degrees.
- If you rotate the camera, repeat the step with the other dimension.
Worked example: a 24 mm lens on full frame and a longer one on APS-C
On full frame, 36 ÷ 48 = 0.75 and atan(0.75) is 36.87°, so the horizontal angle is 73.74°. The height gives 24 ÷ 48 = 0.5, atan 26.57°, vertical angle 53.13°. The diagonal of 43.27 mm gives 84.06°.
On the APS-C preset (23.5 × 15.6 mm) a 35 mm lens gives 37.12° across, 25.13° vertically and 43.89° on the diagonal — close to the 50 mm full-frame figures in the table above, but not identical, because the two sensors have different shapes as well as sizes.
- 24 mm · full frame · horizontal
- 73.74°
- 24 mm · full frame · vertical
- 53.13°
- 35 mm · APS-C · horizontal
- 37.12°
- 35 mm · APS-C · vertical
- 25.13°
Common mistakes
- Comparing a diagonal angle from a lens specification sheet with a horizontal angle from a calculator and concluding that one of them is wrong.
- Planning a tall building with the horizontal angle while shooting in landscape orientation, where the vertical angle is the one that matters.
- Using the equivalent focal length together with the APS-C sensor width, which counts the crop twice.
- Expecting a fisheye or strongly distorted lens to follow the rectilinear tangent formula.
Where the angle stops being reliable
The tangent formula assumes a rectilinear lens focused at infinity. Close focusing, focus breathing, distortion correction and a cropped video mode all change the real frame, so treat these angles as planning numbers and confirm the composition in the viewfinder. Nikon's guide to focal length and angle of view, linked on this page, uses the same width-height distinction.