What this calculator does
Field of view is how much of a scene a camera captures at a given focal length, expressed as an angle in degrees. It depends on two things: the physical size of the sensor recording the image, and the focal length of the lens in front of it. The same lens produces a narrower field of view on a smaller sensor than on a larger one, which is why a "50mm" lens behaves differently on a full-frame camera than on a cropped-sensor one.
The formula is straightforward trigonometry: field of view = 2 × arctan(sensor dimension ÷ (2 × focal length)), applied separately to the sensor's width and height to get the horizontal and vertical angles, and to the sensor's diagonal for the diagonal field of view often quoted on lens specifications.
The formula
Divide the relevant sensor dimension by twice the focal length, take the arctangent of that ratio, then double it to get the full angle rather than the half-angle either side of the lens axis. The calculator applies this separately to sensor width, sensor height and the sensor diagonal (found from width and height with Pythagoras), all in the same units.
| Term | Meaning |
|---|---|
| Sensor width / height | The physical dimensions of the camera's image sensor, commonly in millimetres. |
| Focal length | The distance from the lens's optical centre to the sensor when focused at infinity, in the same units as the sensor. |
| Field of view | The angle of the scene captured, calculated separately for the horizontal, vertical and diagonal directions. |
The inputs explained
| Field | What to enter |
|---|---|
| Sensor width (mm) | The sensor's physical width, in millimetres. A full-frame sensor is 36mm wide; check your camera's specifications for other formats. |
| Sensor height (mm) | The sensor's physical height, in millimetres. Full-frame is 24mm. |
| Focal length (mm) | The lens focal length actually being used, in millimetres, not a "35mm-equivalent" figure unless the sensor size entered is also full-frame. |
When to use it
Choosing a lens for a given shot
Working out the field of view a lens will actually deliver on a specific camera body, before buying it, avoids the common surprise of a lens behaving narrower than expected on a cropped sensor.
Comparing sensor formats at the same focal length
The identical 50mm focal length produces a much wider field of view on a full-frame sensor than on a smaller APS-C or smartphone sensor, since a smaller sensor only captures the central portion of the same projected image.
Planning a fixed camera position
For security cameras, time-lapse rigs or any fixed setup, knowing the exact field of view in degrees tells you how much of a room or scene will actually be captured before installing the equipment.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How field of view narrows as focal length increases, on a full-frame sensor
A standard full-frame sensor, 36mm wide by 24mm high, at a range of common focal lengths.
| Focal length | Horizontal field of view | Vertical field of view |
|---|---|---|
| 20mm | 84.0° | 61.9° |
| 24mm | 73.7° | 53.1° |
| 35mm | 54.4° | 37.8° |
| 50mm | 39.6° | 27.0° |
| 85mm | 23.9° | 16.1° |
| 135mm | 15.2° | 10.2° |
Questions
Why does the same lens look different on different cameras?
Field of view depends on both focal length and sensor size. A smaller sensor only records the central part of the image a lens projects, which narrows the field of view compared with a larger sensor using the same lens.
What is a "35mm-equivalent" focal length?
It restates a lens's field of view in terms of the focal length that would produce the same angle on a full-frame (36mm × 24mm) sensor, which is a common way to compare lenses across different camera formats without doing the trigonometry each time.
Which field of view figure should I use: horizontal, vertical or diagonal?
Horizontal is the most commonly quoted and usually the most useful for framing a scene left to right. Diagonal is often the number printed on lens specifications, since it is the largest of the three and makes for a bigger-sounding figure.
Does this calculator work for smartphone cameras?
Yes, as long as the sensor width and height and the true (not equivalent) focal length are known; smartphone sensors are much smaller than full-frame, typically only a few millimetres across, so their true focal lengths are correspondingly short.
For a telescope and eyepiece combination rather than a camera lens, see the telescope field of view calculator.