# What is my lens’s FOV?

Works out a lens’s horizontal, vertical and diagonal field of view (FOV) from the sensor size and focal length, the area it covers at a distance, and converts a screen FOV between vertical and horizontal for an aspect ratio.

- Page: https://www.acalculator.org/physics/field-of-view-calculator
- JSON spec: https://www.acalculator.org/physics/field-of-view-calculator.json
- Version: 50e3c654cb71

## Default answer

Example with the default inputs (Find Lens FOV, Focal length 50 mm, Sensor width 36 mm, Sensor height 24 mm): The field of view is 39.6° across, 26.99° high and 46.79° on the diagonal.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| mode | Find | A camera lens’s field of view, or a screen’s horizontal field of view from its vertical one (or back). |
| f | Focal length | The lens’s focal length, as marked on the lens (not the 35 mm equivalent). |
| sw | Sensor width | The width of the camera’s sensor or film frame (36 mm for full frame). |
| sh | Sensor height | The height of the sensor or film frame (24 mm for full frame). |
| d | Subject distance | Optional: how far away the subject is, to see the width and height the photo covers there. |
| k | I know the | Which field of view you know: the vertical or the horizontal one. |
| fov | Field of view | The field of view you know, in degrees. |
| aw | Aspect width | The width part of the screen’s aspect ratio, such as 16 in 16:9. |
| ah | Aspect height | The height part of the aspect ratio, such as 9 in 16:9. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| hfov | Horizontal FOV | The angle the picture covers from side to side. |
| vfov | Vertical FOV | The angle the picture covers from top to bottom. |
| dfov | Diagonal FOV | The angle the picture covers from corner to corner. |
| width | Width covered | The width of the scene in the picture at the subject distance. |
| height | Height covered | The height of the scene in the picture at the subject distance. |

## Method

FOV = 2 × arctan(sensor size ÷ (2 × focal length)), for the width, height and diagonal (√(w² + h²)) of the sensor; covered width = distance × sensor width ÷ focal length. Screen: tan(h ÷ 2) = tan(v ÷ 2) × aspect width ÷ aspect height.

## Assumptions

- A rectilinear (not fisheye) lens, focused far away: the image forms one focal length behind the lens. Close focusing narrows the view a little.
- Type the real focal length and the real sensor size, not a 35 mm equivalent.
- The screen mode uses a flat (rectilinear) projection, as games and 3D software do.

## Worked examples

1. mode = lens, f = 0.05, sw = 0.036, sh = 0.024 gives hfov = 0.691111, vfov = 0.47109, dfov = 0.816692. Source: Wikipedia, Angle of view (photography) (α = 2 arctan(d ÷ 2f); a 50 mm lens on a 36 × 24 mm frame: 39.6° horizontal, 27.0° vertical, 46.8° diagonal). https://en.wikipedia.org/wiki/Angle_of_view_(photography), retrieved 2026-10-02: 39.6°, 27.0° and 46.8°; OpenStax, University Physics Volume 3, §2.6 The Camera (thin lens 1/f = 1/dₒ + 1/dᵢ: a distant object images at the focal length). https://openstax.org/books/university-physics-volume-3/pages/2-6-the-camera, retrieved 2026-10-02.
2. mode = lens, f = 0.024, sw = 0.036, sh = 0.024, d = 3.048 gives hfov = 1.287002, width = 4.572, height = 3.048. Source: OpenStax, University Physics Volume 3, §2.6 The Camera (thin lens 1/f = 1/dₒ + 1/dᵢ: a distant object images at the focal length). https://openstax.org/books/university-physics-volume-3/pages/2-6-the-camera, retrieved 2026-10-02.
3. mode = screen, k = v, fov = 1.047198, aw = 16, ah = 9 gives hfov = 1.596851, vfov = 1.047198.

## FAQ

### How do I calculate the field of view of a lens?

FOV = 2 × arctan(sensor size ÷ (2 × focal length)). A 50 mm lens on a 36 × 24 mm full-frame sensor sees 2 × arctan(36 ÷ 100) = 39.6° across and 2 × arctan(24 ÷ 100) = 27.0° from top to bottom.

### Why does a shorter focal length give a wider view?

The sensor stays the same size, so moving it closer to the lens (a shorter focal length) lets it take in a wider angle. A 24 mm lens on full frame sees 73.7° across, nearly twice the angle of a 50 mm lens.

### How much of a scene fits in the picture at a given distance?

Width covered = distance × sensor width ÷ focal length. With a 24 mm lens on full frame, a subject 10 ft away gives a picture 10 × 36 ÷ 24 = 15 ft wide and 10 ft high.

### Does sensor size change the field of view?

Yes. A smaller sensor behind the same lens takes in a narrower angle, which is why smaller sensors are said to have a crop factor. Type your sensor’s real width and height in millimeters.

### How do I convert vertical FOV to horizontal FOV in a game?

Use tan(h ÷ 2) = tan(v ÷ 2) × width ÷ height. A vertical FOV of 60° on a 16:9 screen is a horizontal FOV of 2 × arctan(tan 30° × 16 ÷ 9) = 91.5°.

### What is the diagonal field of view?

The angle from one corner of the picture to the opposite corner. It uses the sensor’s diagonal, √(width² + height²): 43.3 mm on full frame, so 46.8° with a 50 mm lens.

## Sources

- OpenStax, University Physics Volume 3, §2.6 The Camera (thin-lens equation 1/f = 1/dₒ + 1/dᵢ; a distant object images at the focal length). https://openstax.org/books/university-physics-volume-3/pages/2-6-the-camera (retrieved 2026-10-02)
- Wikipedia, Angle of view (photography): α = 2 arctan(d ÷ 2f); a 50 mm lens on a 36 × 24 mm frame covers about 39.6° horizontally, 27.0° vertically and 46.8° diagonally. https://en.wikipedia.org/wiki/Angle_of_view_(photography) (retrieved 2026-10-02)