1/3 inch crop factor and field of view calculator
A 1/3 inch sensor measures 4.8 by 3.6 mm, a diagonal of 6.00 mm. Against the full-frame diagonal of 43.27 mm that is a crop factor of 7.211.
The diagonal divided by this gives the acceptable blur circle. 1500 is the usual modern figure.
- Full-frame equivalent focal length
- 252.39
- Equivalent aperture for depth of field
- 20.191
- Sensor diagonal
- 6.000
- Sensor area
- 17.28 mm2
- Full frame gathers this many times more light
- 50.000
- Horizontal field of view
- 7.845 degrees
- Vertical field of view
- 5.888 degrees
- Diagonal field of view
- 9.798 degrees
- Hyperfocal distance
- 109 410
- Depth of field
- 163
- Frame width at the subject
- 0.411
Show the working
- Focal length = 35
- Aperture f-number = 2.8
- Subject distance = 3
- Circle of confusion divisor = 1500
- sensor_w = 4.8 = 4.8
- sensor_h = 3.6 = 3.6
- Sensor diagonal = hypot(4.8, 3.6) = 6
- Crop factor = 6 > 0 ? 43.266615305567875 / 6 : 0 = 7.2111
- Full-frame equivalent focal length = 35 * 7.2111 = 252.389
- Equivalent aperture for depth of field = 2.8 * 7.2111 = 20.1911
- Sensor area = 4.8 * 3.6 = 17.28
- Full frame gathers this many times more light = 17.28 > 0 ? 864 / 17.28 : 0 = 50
- Horizontal field of view = deg(2 * atan(4.8 / (2 * 35))) = 7.845 43
- Vertical field of view = deg(2 * atan(3.6 / (2 * 35))) = 5.888 09
- Diagonal field of view = deg(2 * atan(6 / (2 * 35))) = 9.798 18
- coc = 6 / 1500 = 0.004
- Hyperfocal distance = 35^2 / (2.8 * 0.004) + 35 = 109 410
- near = 3*1000 * 109 410 / (109 410 + (3*1000 - 35)) = 2920.85
- far = 3*1000 < 109 410 ? 3*1000 * 109 410 / (109 410 - (3*1000 - 35)) : 1e9 = 3083.56
- Depth of field = 3083.56 >= 1e9 ? 1e9 : 3083.56 - 2920.85 = 162.719
- Frame width at the subject = 35 > 0 ? 3 * 4.8 / 35 : 0 = 0.411 429
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 1/3 inch
| Lens | Full-frame equivalent |
|---|---|
| 12 mm | 86.5 mm |
| 16 mm | 115.4 mm |
| 24 mm | 173.1 mm |
| 35 mm | 252.4 mm |
| 50 mm | 360.6 mm |
| 85 mm | 612.9 mm |
| 135 mm | 973.5 mm |
| 200 mm | 1442.2 mm |
Frequently asked
What is the crop factor of a 1/3 inch sensor?
7.211, calculated from its 6.00 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.