Angle of View Calculator
Calculate the angle of view (AoV / FoV) for any lens and sensor size.
Find horizontal, vertical, and diagonal angles for full frame, APS-C, M43, and more.
Angle of View
The angle of view (AoV) — sometimes called field of view (FoV) — is the angular extent of the scene captured by a lens-and-sensor combination. A wider angle includes more of the scene; a narrower angle magnifies a small portion.
Formula
AoV = 2 × arctan(d / (2 × f))
Where:
- d = relevant sensor dimension (width, height, or diagonal in mm)
- f = focal length in mm
For a full-frame sensor (36 × 24 mm) and a 50 mm lens:
- Horizontal AoV = 2 × arctan(36 / 100) = 39.6°
- Vertical AoV = 2 × arctan(24 / 100) = 27.0°
- Diagonal AoV = 2 × arctan(43.27 / 100) = 46.8°
Common Lens Categories
| Diagonal AoV | Category | Typical Focal Length (FF) |
|---|---|---|
| > 90° | Ultra-wide | < 18 mm |
| 65–90° | Wide | 18–28 mm |
| 50–65° | Standard wide | 28–35 mm |
| 40–50° | Standard (“normal”) | 40–55 mm |
| 25–40° | Short telephoto | 60–105 mm |
| 10–25° | Telephoto | 105–300 mm |
| < 10° | Super telephoto | > 300 mm |
The “normal” focal length for any sensor is roughly equal to its diagonal — 43 mm for full-frame, 28 mm for APS-C, 21 mm for Micro Four Thirds.
Common Sensor Sizes
| Sensor | Width × Height (mm) | Diagonal (mm) | Crop factor |
|---|---|---|---|
| Full-frame (35mm) | 36 × 24 | 43.27 | 1.0 |
| APS-C (Canon) | 22.3 × 14.9 | 26.82 | 1.61 |
| APS-C (Nikon/Sony) | 23.6 × 15.6 | 28.30 | 1.53 |
| Micro Four Thirds | 17.3 × 13 | 21.64 | 2.00 |
| 1-inch (compact) | 13.2 × 8.8 | 15.86 | 2.73 |
| Phone (1/2.55") | 5.76 × 4.29 | 7.18 | 6.03 |
Equivalent Focal Length
To compare lenses across sensor sizes, multiply by the crop factor:
- 50 mm on Micro Four Thirds = 100 mm equivalent on full frame
- 35 mm on APS-C ≈ 53 mm equivalent on full frame
This is what camera manufacturers mean by “35 mm equivalent focal length.”
Worked Example — Wide-Angle Real Estate Lens
A 14 mm lens on full frame:
- Diagonal AoV = 2 × arctan(43.27 / 28) = 114.2°
That is dramatic — almost peripheral vision wide. Useful for tight interiors but introduces strong perspective distortion at edges.
Caveats
The simple formula assumes a rectilinear lens — straight lines stay straight in the projection. Fisheye lenses use stereographic or equidistant projections and have AoV up to 180°+ at the diagonal, exceeding what the rectilinear formula predicts. For long-distance scenes, atmospheric refraction, vignetting, and lens distortion all introduce small departures from the geometric AoV.
Quick Mental Check
Doubling focal length roughly halves the angle of view (for moderate AoV). Halving sensor diagonal also halves AoV — equivalent to multiplying focal length by 2 (i.e. crop factor 2). This is the geometric origin of “crop factor” pricing in lens lineups.