Field of View Calculator (focal length & sensor)

Understanding the field of view calculator — concept and principle

This calculator finds the angle of view of a lens, horizontally, vertically and diagonally, from its focal length and the camera's sensor size. It also gives the full-frame equivalent focal length. Use it to know how much of a scene a lens will cover before buying it or choosing where to stand.

How it is calculated

Angle of view = 2 × arctan(d ÷ (2f))

• f is the focal length in mm.
• d is the sensor dimension in mm: width for horizontal, height for vertical, and the diagonal √(width² + height²) for diagonal.
• Full-frame equivalent focal length = f × √(36² + 24²) ÷ sensor diagonal, where 43.27 mm is the diagonal of a 36 × 24 mm frame. The ratio 43.27 ÷ diagonal is the crop factor.

Angles are shown in degrees.

The principle

A rectilinear lens focused at infinity forms an image one focal length behind its optical centre. Rays from the edges of the field pass through that centre and land on the edges of the sensor, forming a right triangle with the half-sensor dimension (d/2) as the opposite side and f as the adjacent side. The half angle is therefore arctan(d / 2f), and doubling it gives the full angle. A shorter focal length or a larger sensor widens the angle. Because a smaller sensor crops the centre of the image, the same lens looks "longer" on it; the crop factor expresses that.

Worked example

Defaults: 50 mm lens on full frame (36 × 24 mm).

1. Horizontal: 2 × arctan(36 / 100) = 2 × 19.799° ≈ 39.59775271°.
2. Vertical: 2 × arctan(24 / 100) ≈ 26.99146656°.
3. Diagonal: √(36² + 24²) = 43.2666 mm; 2 × arctan(43.2666 / 100) ≈ 46.79300334°.
4. Equivalent focal length: 50 × 43.2666 ÷ 43.2666 = 50 mm, as expected for a full-frame sensor.

These match the calculator's output.

How to read the result

Rough guide by diagonal angle: above about 75° is wide-angle (24 mm on full frame is about 84°), around 40–60° is "normal", similar to the natural feel of human vision in a photo, and below about 30° is telephoto. Lens makers usually quote the diagonal angle, so use that one when comparing with specifications. To know how wide an area a lens covers at a distance D, use 2 × D × tan(angle / 2); at 10 m, the 50 mm horizontal coverage is about 7.2 m.

Common mistakes

• Comparing your horizontal angle with a manufacturer's diagonal figure.
• Applying the formula to fisheye lenses, which do not follow rectilinear projection.
• Forgetting that video modes often crop the sensor, narrowing the angle.

Frequently asked questions

What is the field of view of a 50 mm lens on full frame?

About 39.6° horizontally, 27.0° vertically and 46.8° diagonally.

Why does the same lens look more zoomed in on APS-C?

The smaller sensor records only the central part of the image, so the angle is narrower, as if the focal length were about 1.5 times longer.

Does focusing closer change the field of view?

Yes, slightly. Many lenses narrow or widen a little as they focus closer (focus breathing).

Sources: S. F. Ray, Applied Photographic Optics, Focal Press · R. Kingslake, Optics in Photography, SPIE Press