full frame crop factor and field of view calculator
A full frame sensor measures 36 by 24 mm, a diagonal of 43.27 mm. Against the full-frame diagonal of 43.27 mm that is a crop factor of 1.000. The reference format: 35 mm film, and the one crop factors are quoted against.
The diagonal divided by this gives the acceptable blur circle. 1500 is the usual modern figure.
- Full-frame equivalent focal length
- 35.00
- Equivalent aperture for depth of field
- 2.800
- Sensor diagonal
- 43.267
- Sensor area
- 864.00 mm2
- Full frame gathers this many times more light
- 1.000
- Horizontal field of view
- 54.432 degrees
- Vertical field of view
- 37.849 degrees
- Diagonal field of view
- 63.440 degrees
- Hyperfocal distance
- 15 203
- Depth of field
- 1216
- Frame width at the subject
- 3.086
Show the working
- Focal length = 35
- Aperture f-number = 2.8
- Subject distance = 3
- Circle of confusion divisor = 1500
- sensor_w = 36 = 36
- sensor_h = 24 = 24
- Sensor diagonal = hypot(36, 24) = 43.2666
- Crop factor = 43.2666 > 0 ? 43.266615305567875 / 43.2666 : 0 = 1
- Full-frame equivalent focal length = 35 * 1 = 35
- Equivalent aperture for depth of field = 2.8 * 1 = 2.8
- Sensor area = 36 * 24 = 864
- Full frame gathers this many times more light = 864 > 0 ? 864 / 864 : 0 = 1
- Horizontal field of view = deg(2 * atan(36 / (2 * 35))) = 54.4322
- Vertical field of view = deg(2 * atan(24 / (2 * 35))) = 37.8493
- Diagonal field of view = deg(2 * atan(43.2666 / (2 * 35))) = 63.44
- coc = 43.2666 / 1500 = 0.028 844 4
- Hyperfocal distance = 35^2 / (2.8 * 0.028 844 4) + 35 = 15 202.6
- near = 3*1000 * 15 202.6 / (15 202.6 + (3*1000 - 35)) = 2510.39
- far = 3*1000 < 15 202.6 ? 3*1000 * 15 202.6 / (15 202.6 - (3*1000 - 35)) : 1e9 = 3726.86
- Depth of field = 3726.86 >= 1e9 ? 1e9 : 3726.86 - 2510.39 = 1216.47
- Frame width at the subject = 35 > 0 ? 3 * 36 / 35 : 0 = 3.085 71
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- crop factor = full-frame diagonal / sensor diagonal
- field of view = 2 arctan(sensor dimension / 2 focal length)
- hyperfocal distance = f^2 / (N c) + f
- equivalent aperture = aperture x crop factor, for depth of field and total light
Crop factor changes the framing, not the lens. A 50 mm lens is always a 50 mm lens; it just sees a smaller rectangle.
Equivalent aperture matters for depth of field and total light gathered, not for exposure. An f/2.8 lens meters as f/2.8 on any format.
The circle of confusion is a judgement about acceptable sharpness at a viewing size, not a physical constant.
The reference format: 35 mm film, and the one crop factors are quoted against.
Equivalent focal lengths on full frame
| Lens | Full-frame equivalent |
|---|---|
| 12 mm | 12.0 mm |
| 16 mm | 16.0 mm |
| 24 mm | 24.0 mm |
| 35 mm | 35.0 mm |
| 50 mm | 50.0 mm |
| 85 mm | 85.0 mm |
| 135 mm | 135.0 mm |
| 200 mm | 200.0 mm |
Frequently asked
What is the crop factor of a full frame sensor?
1.000, calculated from its 43.27 mm diagonal against full frame at 43.27 mm.
Does a crop sensor make a lens longer?
No. The lens projects the same image; the smaller sensor simply records a smaller part of it, which looks like a longer lens.