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Angle of View / Crop Factor Calculator

Calculate a lens's horizontal, vertical, and diagonal angle of view plus crop factor and 35mm-equivalent focal length, from focal length and sensor dimensions.

Diagonal angle of view
46.8°
Horizontal angle of view
39.6°
Vertical angle of view
27°
Crop factor (vs. 35mm full frame)
1x
35mm-equivalent focal length
50 mm

How it works

Angle of view = 2 × arctan(sensor dimension ÷ (2 × focal length)), applied separately to the sensor's width, height, and diagonal (diagonal = √(width² + height²)) to get the horizontal, vertical, and diagonal angles. Verified via web search against Wikipedia's Angle of view reference rather than relied on from memory — this reproduces the well-known ~46.8° diagonal angle of view for a 50mm lens on a full-frame (36×24mm) sensor.

Crop factor compares a sensor's diagonal to the 35mm 'full frame' reference diagonal (36×24mm, diagonal ≈43.27mm): crop factor = full-frame diagonal ÷ this sensor's diagonal. Multiplying a lens's actual focal length by the crop factor gives its '35mm-equivalent' focal length — the focal length that would produce the same angle of view on a full-frame sensor. This reproduces Canon APS-C's commonly cited ~1.61x crop factor and Micro Four Thirds' near-exact 2.0x crop factor from their published sensor dimensions.

Focal length and sensor dimensions are always specified in millimeters industry-wide, regardless of a country's customary unit system, so there's no metric/imperial toggle here — the same reasoning this site's Depth of Field calculator already applies to its own focal-length input.

FAQ

Where do I find my camera's sensor dimensions?

They're published in your camera's spec sheet (search '[camera model] sensor size mm'). Common reference sizes: full frame is 36×24mm, Canon APS-C is about 22.3×14.9mm, most other APS-C (Nikon, Sony, Fujifilm) is about 23.5×15.6mm, and Micro Four Thirds is 17.3×13mm.

What is crop factor actually used for?

It lets you compare lenses across different camera sensor sizes using a common reference. A 50mm lens frames a noticeably tighter shot on a crop-factor-2.0x Micro Four Thirds camera than on a full-frame camera, even though the physical focal length is identical — multiplying by the crop factor (giving a '100mm full-frame equivalent') tells you what full-frame lens would produce the same framing.

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