How do you calculate a camera's field of view?

The angle of view is twice the arctangent of half the sensor dimension divided by the focal length. Use the sensor width for the horizontal angle, the height for the vertical angle, and the diagonal for the diagonal angle. The real width covered at a distance is the sensor width times the distance divided by the focal length.

What is the field of view of a 50mm lens?

On a full-frame 36 by 24 millimetre sensor, a 50 mm lens has a horizontal angle of view of about 39.6 degrees, a vertical angle of about 27 degrees, and a diagonal of about 47 degrees. This is close to the perspective of the human eye, which is why 50 mm is called a standard lens.

Does sensor size change the field of view?

Yes. For the same focal length, a smaller sensor captures a narrower field of view, effectively cropping the image. A 50 mm lens that gives a standard view on full-frame acts like a short telephoto on a smaller APS-C or micro four thirds sensor, because the smaller sensor sees less of the projected image.

Camera Field of View Calculator

This camera field of view calculator works out how much of a scene a lens will capture, both as an angle of view in degrees and as the real width and height it covers at a given distance. Field of view depends on two things: the focal length of the lens and the size of the camera's sensor. A short focal length or a large sensor gives a wide view, while a long focal length or a small sensor gives a narrow, magnified view. You enter the focal length in millimetres, the sensor width and height in millimetres, and the distance to your subject, and the calculator returns the horizontal, vertical and diagonal angles of view, along with the width and height of the frame at that distance. The angle of view comes from the geometry of the sensor and lens, and the frame size at a distance follows from similar triangles. Photographers and videographers use it to choose a lens for a shot, to work out how far back to stand, to plan security camera coverage, and to compare how the same lens behaves on full-frame, APS-C and micro four thirds bodies. The defaults describe a 50 mm lens on a full-frame 36 by 24 millimetre sensor, the classic standard view. Change the sensor size to match your own camera.

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Focal length

Sensor width

Sensor height

Subject distance

39.6°

horizontal angle of view

Vertical AoV27.0°

Diagonal AoV46.8°

Frame at distance2.16 x 1.44 m

A 50 mm lens on a 36 x 24 mm sensor sees 39.6° across and 27.0° vertically (46.8° diagonally). At 3 m that frames an area about 2.16 m wide by 1.44 m high.

Angles are the geometric field of view of the sensor. Real lenses can show slight distortion and breathing that shift the exact framing. Indicative only.

How it works

The angle of view is found from a right-angle triangle formed by the sensor and the focal length. For each sensor dimension, the half-angle is the arctangent of half that dimension divided by the focal length, and doubling it gives the full angle of view. Doing this with the sensor width gives the horizontal angle, with the height gives the vertical angle, and with the sensor diagonal gives the diagonal angle, the one lens makers usually quote. The real-world coverage at a distance comes from similar triangles: the frame width equals the sensor width times the distance divided by the focal length, and the same relationship gives the height. Because both the angle and the coverage scale with sensor size, the same 50 mm lens is a standard view on full-frame but a short telephoto on a smaller APS-C sensor.

Worked example

Take a 50 mm lens on a full-frame sensor measuring 36 by 24 millimetres, focused on a subject 3 metres away. The horizontal angle of view is twice the arctangent of 18 divided by 50, which is about 39.6 degrees. The vertical angle, using half of 24, is about 27.0 degrees, and the diagonal, using the 43.3 millimetre sensor diagonal, is about 46.8 degrees. At 3 metres the frame is 36 times 3 divided by 50, which is 2.16 metres wide, and 24 times 3 divided by 50, which is 1.44 metres high. That is why a 50 mm lens is called a standard lens: its view is close to what the eye sees as natural.

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Angle Conversion Calculator: degrees and radians.

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