What the angle of view tells you
The angle of view of a lens is how wide a slice of the scene it captures. It depends on two things only: the focal length and the size of the sensor. The same 35 mm lens is a moderate wide angle on a full-frame camera but a normal lens on an APS-C camera, because the smaller sensor records only the center of the image.
The formula
For each dimension of the sensor (width, height or diagonal):
angle = 2 × arctan(sensor dimension ÷ (2 × focal length))
At a given distance, the area the frame covers is approximately:
width = distance × sensor width ÷ focal length
This approximation is accurate for subjects much farther away than the focal length; it is not meant for macro photography.
Worked example
A 35 mm lens on a full-frame camera (36 × 24 mm), with a subject 30 ft away:
| Result | Value |
|---|---|
| Horizontal angle | 54.4° |
| Vertical angle | 37.8° |
| Diagonal angle | 63.4°, a moderate wide angle |
| Width covered at 30 ft | 30.86 ft |
| Height covered at 30 ft | 20.57 ft |
On an APS-C camera (23.5 mm wide), the same lens covers only about 37° horizontally and behaves like a 54 mm lens on full frame.
Crop factor and equivalent focal length
The crop factor is the ratio between the full-frame diagonal, 43.27 mm, and your sensor’s diagonal:
| Sensor | Size (mm) | Crop factor |
|---|---|---|
| Full frame | 36 × 24 | 1.0 |
| APS-C (Nikon, Sony, Fujifilm) | 23.5 × 15.6 | about 1.5 |
| APS-C (Canon) | 22.3 × 14.9 | about 1.6 |
| Micro Four Thirds | 17.3 × 13 | 2.0 |
| 1-inch | 13.2 × 8.8 | about 2.7 |
| Medium format 44 × 33 | 44 × 33 | about 0.79 |
Multiply the focal length by the crop factor to get the full-frame lens with the same angle of view.
Typical angles on full frame
| Focal length | Horizontal angle | Common name |
|---|---|---|
| 14 mm | 104° | Ultra wide |
| 24 mm | 74° | Wide |
| 50 mm | 40° | Normal |
| 85 mm | 24° | Short telephoto, portraits |
| 200 mm | 10° | Telephoto |
| 600 mm | 3.4° | Super telephoto, wildlife |
Tips
- Use the field width to plan a shot: for example, which focal length frames a 20-ft stage from the back of a room.
- Zoom lenses at close focus can have a slightly narrower angle than their marked focal length, an effect called focus breathing.