Apertia · Library
When is diagonal field of view useful, and when is it misleading?
A 50 mm lens on full frame and 25 mm on Micro Four Thirds both cover 46.8° diagonally, yet their vertical angles are 27.0° and 29.1°.
One angle per side, one across corners
The field-of-view tool reports three angles from the same rectilinear formula, angle = 2 × atan(size ÷ (2f)): horizontal from the sensor width, vertical from the height, and diagonal from the corner-to-corner length. The Apertia calculator shows only the horizontal angle under the focal-length ring. Lens specifications usually quote the diagonal, which is why the same lens can seem to have two different angles.
The diagonal is a single summary of a rectangle. Two formats with equal diagonals but different aspect ratios split that angle differently between width and height.
Worked example
The 36 × 24 mm, 50 mm model reports about 46.793° diagonally. Its 39.598° horizontal and 26.991° vertical angles remain different quantities.
- Diagonal angle (degrees)
- 46.793003
- Horizontal angle (degrees)
- 39.597753
- Vertical angle (degrees)
- 26.991467
Use the angle that matches the task
- Decide which edge limits the shot: a wide facade needs the horizontal angle, a tall tree the vertical one.
- Read that angle for your sensor and actual focal length.
- Use the diagonal only to compare with a lens maker's specification.
- For a subject at a known distance, check the scene width and height instead of the angles.
Worked example: equal diagonals
A 50 mm lens on the 36 × 24 mm full-frame preset covers 46.8 degrees across the diagonal, 39.6 degrees horizontally and 27.0 degrees vertically. A 25 mm lens on the 17.3 × 13 mm Micro Four Thirds preset also covers 46.8 degrees diagonally, but 38.2 degrees horizontally and 29.1 degrees vertically. The 4:3 frame trades 1.4 degrees of width for 2.1 degrees of height.
- Full frame, 50 mm
- 46.8° · 39.6° · 27.0°
- Micro Four Thirds, 25 mm
- 46.8° · 38.2° · 29.1°
- Order
- diagonal · horizontal · vertical
Common mistakes
- Comparing the app's horizontal angle with a diagonal figure from a lens box.
- Concluding that two lenses frame identically because their diagonal angles match.
- Using infinity angles for a close-up, where the thin-lens scene size is smaller than the angle suggests.
- Forgetting to swap horizontal and vertical when the camera is turned to portrait.
Scope of the angles
All three angles assume focus at infinity and an undistorted rectilinear lens. Fisheye projection, distortion correction and focus breathing are outside the model; the Nikon angle-of-view guide and the DOFMaster equations below describe the ideal relation.