1/2.5 inch crop factor and field of view calculator
A 1/2.5 inch sensor measures 5.76 by 4.29 mm, a diagonal of 7.18 mm. Against the full-frame diagonal of 43.27 mm that is a crop factor of 6.024.
The diagonal divided by this gives the acceptable blur circle. 1500 is the usual modern figure.
- Full-frame equivalent focal length
- 210.85
- Equivalent aperture for depth of field
- 16.868
- Sensor diagonal
- 7.182
- Sensor area
- 24.71 mm2
- Full frame gathers this many times more light
- 34.965
- Horizontal field of view
- 9.408 degrees
- Vertical field of view
- 7.014 degrees
- Diagonal field of view
- 11.716 degrees
- Hyperfocal distance
- 91 409
- Depth of field
- 195
- Frame width at the subject
- 0.494
Show the working
- Focal length = 35
- Aperture f-number = 2.8
- Subject distance = 3
- Circle of confusion divisor = 1500
- sensor_w = 5.76 = 5.76
- sensor_h = 4.29 = 4.29
- Sensor diagonal = hypot(5.76, 4.29) = 7.182 04
- Crop factor = 7.182 04 > 0 ? 43.266615305567875 / 7.182 04 : 0 = 6.024 28
- Full-frame equivalent focal length = 35 * 6.024 28 = 210.85
- Equivalent aperture for depth of field = 2.8 * 6.024 28 = 16.868
- Sensor area = 5.76 * 4.29 = 24.7104
- Full frame gathers this many times more light = 24.7104 > 0 ? 864 / 24.7104 : 0 = 34.965
- Horizontal field of view = deg(2 * atan(5.76 / (2 * 35))) = 9.408 05
- Vertical field of view = deg(2 * atan(4.29 / (2 * 35))) = 7.014 05
- Diagonal field of view = deg(2 * atan(7.182 04 / (2 * 35))) = 11.7162
- coc = 7.182 04 / 1500 = 0.004 788 03
- Hyperfocal distance = 35^2 / (2.8 * 0.004 788 03) + 35 = 91 408.8
- near = 3*1000 * 91 408.8 / (91 408.8 + (3*1000 - 35)) = 2905.75
- far = 3*1000 < 91 408.8 ? 3*1000 * 91 408.8 / (91 408.8 - (3*1000 - 35)) : 1e9 = 3100.57
- Depth of field = 3100.57 >= 1e9 ? 1e9 : 3100.57 - 2905.75 = 194.825
- Frame width at the subject = 35 > 0 ? 3 * 5.76 / 35 : 0 = 0.493 714
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.
Equivalent focal lengths on 1/2.5 inch
| Lens | Full-frame equivalent |
|---|---|
| 12 mm | 72.3 mm |
| 16 mm | 96.4 mm |
| 24 mm | 144.6 mm |
| 35 mm | 210.8 mm |
| 50 mm | 301.2 mm |
| 85 mm | 512.1 mm |
| 135 mm | 813.3 mm |
| 200 mm | 1204.9 mm |
Frequently asked
What is the crop factor of a 1/2.5 inch sensor?
6.024, calculated from its 7.18 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.