Calculate camera angle of view, frame size at distance, or required focal length from sensor format, focal length, and subject distance.
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Angle of View Formula
The calculator uses one core trigonometric relationship and rearranges it for each mode.
AOV = 2 * arctan(d / (2 * f))
Frame size mode:
Frame = D * d / f
Focal length mode:
f = d * D / Frame
- AOV = angle of view in degrees (horizontal, vertical, or diagonal)
- d = sensor dimension (width, height, or diagonal) in mm
- f = lens focal length in mm
- D = subject distance in mm
- Frame = the width, height, or diagonal of the scene captured at distance D
Assumptions: the formula treats the lens as a thin lens focused at infinity, ignores distortion, and assumes the subject distance is much larger than the focal length. At very close (macro) distances the effective focal length grows and real coverage will be slightly narrower than the calculated value. The 35mm-equivalent focal length shown in results scales by the ratio of the full-frame diagonal (43.27 mm) to your sensor diagonal.
Reference Tables
Diagonal angle of view for common focal lengths on popular sensor formats:
| Focal length | Full-frame | APS-C (Sony) | MFT | 1-inch |
|---|---|---|---|---|
| 14 mm | 114° | 90° | 75° | 59° |
| 24 mm | 84° | 61° | 47° | 36° |
| 35 mm | 63° | 44° | 33° | 25° |
| 50 mm | 47° | 31° | 24° | 18° |
| 85 mm | 29° | 19° | 14° | 11° |
| 200 mm | 12° | 8° | 6° | 5° |
How a diagonal angle translates to lens character on a full-frame body:
| Diagonal AOV | Lens type | Typical use |
|---|---|---|
| Above 90° | Ultra-wide | Interiors, real estate, astro |
| 63° to 84° | Wide | Landscape, environmental |
| 40° to 63° | Normal | Documentary, street, video |
| 18° to 40° | Short telephoto | Portraits, products |
| 8° to 18° | Telephoto | Sports, wildlife |
| Below 8° | Super-telephoto | Distant wildlife, surveillance |
Worked Example
A 50 mm lens on a full-frame sensor (36 × 24 mm, diagonal 43.27 mm):
- Horizontal: 2 × arctan(36 / 100) = 39.6°
- Vertical: 2 × arctan(24 / 100) = 27.0°
- Diagonal: 2 × arctan(43.27 / 100) = 46.8°
Standing 3 m from the subject, the frame covers 3 × 36 / 50 = 2.16 m wide by 1.44 m tall. To fit a 2 m wide subject from that same 3 m distance, you need 36 × 3000 / 2000 = 54 mm.
FAQ
Why are three angles reported? Lens specs usually quote the diagonal value because it is the largest, but the horizontal and vertical angles tell you what fits left-to-right and top-to-bottom. Use diagonal for comparing lenses, horizontal or vertical for framing real subjects.
Does the angle change when I focus closer? Yes, slightly. Internal focusing lenses can lose a few degrees at minimum focus distance. The change is negligible for normal shooting distances and only matters for macro work.
How does crop factor relate to this? Crop factor is the ratio of the full-frame diagonal to your sensor diagonal. Multiplying your focal length by the crop factor gives the full-frame focal length that produces the same angle of view, which is the "35mm equivalent" shown in the results.
