absurdtools

Field of View & Crop Factor Calculator

Angle of view and crop factor for any lens and sensor — where halving the focal length gives 1.81 times the angle, not two, and the shortfall grows.

These are the rectilinear angles a normal lens gives. A fisheye maps the scene differently and fits far more into the frame than the formula predicts, so its stated focal length will not match anything here. Nothing is uploaded.

Halving the focal length never doubles the angle

Angle of view is an arctangent, not a reciprocal — so the shortfall against the proportional guess gets worse the wider you go. Going 400 mm to 200 mm gives 1.996× the angle, near enough two. Going 50 to 25 gives 1.806. Going 12.5 to 6.25 gives only 1.283, and the function can never reach 180° however short the lens. So the rule of thumb is asymptotically right for long lenses and fails exactly where people reach for it — choosing between wide ones.

HalvingFromToRatio
400 mm → 200 mm 5.15° 10.29° 1.9960×
200 mm → 100 mm 10.29° 20.41° 1.9841×
100 mm → 50 mm 20.41° 39.60° 1.9403×
50 mm → 25 mm 39.60° 71.51° 1.8059×
25 mm → 12.5 mm 71.51° 110.44° 1.5445×
12.5 mm → 6.25 mm 110.44° 141.70° 1.2830×

Which is why the jump from a 24 mm to a 16 mm feels smaller than the numbers promise, and the jump from a 200 mm to a 300 mm is very nearly what they promise. Coverage, on the other hand, is strictly proportional to distance — twice as far away is exactly twice as wide a scene.

LensHorizontalDiagonalCovers at 10 m
12 mm 112.62° 121.97° 30.00 m
16 mm 96.73° 107.03° 22.50 m
24 mm 73.74° 84.06° 15.00 m
35 mm 54.43° 63.44° 10.29 m
50 mm 39.60° 46.79° 7.20 m
85 mm 23.91° 28.56° 4.24 m
135 mm 15.19° 18.21° 2.67 m
200 mm 10.29° 12.35° 1.80 m

A crop sensor does not lengthen your lens — it crops

The crop factor is nothing but a width ratio, and the equivalence it gives is exact — a 50 mm on APS-C frames precisely like a 76.3 mm on full frame, to the last decimal. But it is an equivalence of angle only. The lens is unchanged: it is still a 50 mm, projecting the same image, and the smaller sensor is simply taking a smaller piece of it. Perspective is set by where you stand and depth of field by the real focal length and the real aperture, so neither comes along with the equivalent number.

FormatWidthCrop50 mm givesFrames like
Full frame 36 mm 1.000× 39.60° 50.0 mm
APS-C 23.6 mm 1.525× 26.56° 76.3 mm
Micro Four Thirds 17.3 mm 2.081× 19.63° 104.0 mm
1 inch 13.2 mm 2.727× 15.04° 136.4 mm

How to use

  1. Enter your focal length and sensor width.
  2. Enter a subject distance if you want the coverage.
  3. Read the horizontal and diagonal angles.
  4. Compare against other focal lengths in the table.

Frequently asked questions

Does halving the focal length double the angle of view?

No, and it never does. Angle of view is an arctangent, so 50 mm to 25 mm gives 1.806 times the angle and 25 mm to 12.5 mm gives only 1.544. The function saturates and can never pass 180 degrees.

When is the rule of thumb about right?

At the long end. Going 400 mm to 200 mm gives 1.996 times the angle, which is near enough two for any purpose. It fails exactly where people reach for it — choosing between wide lenses, where the gap is much smaller than the numbers suggest.

What is a crop factor?

Nothing but a width ratio against full frame 36 mm. APS-C at 23.6 mm is 1.525, Micro Four Thirds 2.081, a 1 inch sensor 2.727. Multiply your focal length by it to get the full-frame lens that frames the same way.

Does a crop sensor turn my 50 mm into a 75 mm?

Only in framing. A 50 mm on APS-C gives exactly the angle a 76.3 mm gives on full frame — but the lens is unchanged. The smaller sensor is taking a smaller piece of the same projected image, which is a crop rather than a magnification.

So what does NOT come with the equivalence?

Perspective and depth of field. Perspective is set by where you stand, and depth of field by the real focal length and real aperture. Only the angle transfers, which is why "equivalent" causes so much confusion.

How wide a scene will I get at a given distance?

Coverage is strictly proportional to distance — twice as far away is exactly twice as wide. A 50 mm on full frame covers about 7.2 metres at ten metres, and 14.4 at twenty.

Why is the diagonal angle bigger?

Because the diagonal of the sensor is longer than its width, and the angle follows whichever dimension you measure. Manufacturers usually quote the diagonal, which is why a lens sounds wider on the box than it looks across the frame.

Does this send anything anywhere?

No. Every figure is computed in your browser, and nothing is uploaded or stored.

🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.