Field of View Calculator: Angle of View and Covered Width

How to use it

Choose the Sensor of your camera. For another size, choose Other size (type it) and type the Sensor width and Sensor height in millimetres.
Type the Focal length that the lens is set to, in millimetres.
Type the Distance to the subject, in metres.
Read the Horizontal angle of view, the Vertical angle of view, the Diagonal angle of view and the Width covered at the distance.
Use the table to compare the same sensor at other focal lengths.

How the angle of view is calculated

For a sensor dimension S and a focal length f, the angle of view is 2 × arctan(S ÷ 2f), with both lengths in the same unit. The OpenMV field-of-view documentation gives this formula and derives it from the thin-lens model. The horizontal, vertical and diagonal angles use the width, the height and the diagonal of the sensor.

At a subject distance d the picture covers S × d ÷ f. This is the same geometry without the arctangent: 2 × d × tan(angle ÷ 2) gives the same value. A 50 mm lens on a full-frame sensor at 5 m therefore covers 35.9 × 5,000 ÷ 50 = 3,590 mm, which is 3.59 m.

angle = 2 × arctan(S ÷ (2 × f))
covered length = S × d ÷ f
diagonal S = √(width² + height²)

Sensor sizes used

The full-frame size of 35.9 × 23.9 mm is in the Nikon Z6III specifications, and the Canon EOS R6 manual gives approx. 35.9 × 23.9 mm for full-frame shooting. The Nikon D7500 technical notes give 23.5 × 15.7 mm for the DX format, and the OM System OM-1 Mark II specifications give 17.3 × 13.0 mm for its 4/3 sensor.

Sensor sizes differ between makers and models, so the specification sheet of your own camera is the figure to use. The Other size choice takes any width and height.

What the calculator does not cover

Lenses that do not follow the thin-lens model, such as very wide or special lenses. The formula is derived from that model.
Distortion: real lenses bend straight lines near the edges of the picture, so the corners can differ from these figures.
Crop modes: a mode that uses a smaller part of the sensor gives a narrower angle. Type that part of the sensor as the Other size.

Worked example: 50 mm on full frame at 5 m

The horizontal angle is 2 × arctan(35.9 ÷ 100) = 39.5 degrees. The vertical angle is 26.9 degrees and the diagonal angle is 46.7 degrees. At 5 m the picture covers 35.9 × 5 ÷ 50 = 3.59 m across and 23.9 × 5 ÷ 50 = 2.39 m high.

Output	Value
Horizontal angle of view	39.5 degrees
Vertical angle of view	26.9 degrees
Diagonal angle of view	46.7 degrees
Width covered at 5 m	3.59 m
Height covered at 5 m	2.39 m

Frequently asked questions

What is the angle of view?

The angle of view is the angle of the scene that a lens and a sensor take in. It is measured for the long side, the short side and the diagonal of the sensor, which gives three angles for one lens.

Why does the same lens give a narrower angle on a smaller sensor?

The sensor size is part of the formula: a smaller sensor takes in a smaller part of the image that the lens forms, so the same focal length gives a smaller angle. The crop factor tool compares a smaller sensor with full frame at the same focal length.

Does the covered width depend on the distance?

Yes. The covered width grows in proportion to the distance: at twice the distance the picture covers twice the width, while the angle of view stays the same.

Why can the angles differ from the figures in a lens specification?

The sensor size, the distortion of the lens and the focus distance can differ from the values used here, and this calculator uses the thin-lens formula. For a precise figure, check the specification of your own camera or lens.

Which sensor size should I enter?

Enter the sensor size from your camera specification sheet. The three presets use the sizes from the manufacturer pages named in the sources; for any other camera, choose Other size and type its width and height.

Does the formula work for fisheye lenses?

The formula is derived from the thin-lens model, and very wide or special lenses can depart from that model. Do not rely on this calculator for the exact angle of a fisheye lens.

Sources

Figures and text last checked on Thursday, November 12, 2026.

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