2/3 inch crop factor and field of view calculator
A 2/3 inch sensor measures 8.8 by 6.6 mm, a diagonal of 11.00 mm. Against the full-frame diagonal of 43.27 mm that is a crop factor of 3.933.
The diagonal divided by this gives the acceptable blur circle. 1500 is the usual modern figure.
- Full-frame equivalent focal length
- 137.67
- Equivalent aperture for depth of field
- 11.013
- Sensor diagonal
- 11.000
- Sensor area
- 58.08 mm2
- Full frame gathers this many times more light
- 14.876
- Horizontal field of view
- 14.331 degrees
- Vertical field of view
- 10.773 degrees
- Diagonal field of view
- 17.861 degrees
- Hyperfocal distance
- 59 694
- Depth of field
- 299
- Frame width at the subject
- 0.754
Show the working
- Focal length = 35
- Aperture f-number = 2.8
- Subject distance = 3
- Circle of confusion divisor = 1500
- sensor_w = 8.8 = 8.8
- sensor_h = 6.6 = 6.6
- Sensor diagonal = hypot(8.8, 6.6) = 11
- Crop factor = 11 > 0 ? 43.266615305567875 / 11 : 0 = 3.933 33
- Full-frame equivalent focal length = 35 * 3.933 33 = 137.667
- Equivalent aperture for depth of field = 2.8 * 3.933 33 = 11.0133
- Sensor area = 8.8 * 6.6 = 58.08
- Full frame gathers this many times more light = 58.08 > 0 ? 864 / 58.08 : 0 = 14.876
- Horizontal field of view = deg(2 * atan(8.8 / (2 * 35))) = 14.3306
- Vertical field of view = deg(2 * atan(6.6 / (2 * 35))) = 10.7725
- Diagonal field of view = deg(2 * atan(11 / (2 * 35))) = 17.8612
- coc = 11 / 1500 = 0.007 333 33
- Hyperfocal distance = 35^2 / (2.8 * 0.007 333 33) + 35 = 59 694.1
- near = 3*1000 * 59 694.1 / (59 694.1 + (3*1000 - 35)) = 2858.04
- far = 3*1000 < 59 694.1 ? 3*1000 * 59 694.1 / (59 694.1 - (3*1000 - 35)) : 1e9 = 3156.8
- Depth of field = 3156.8 >= 1e9 ? 1e9 : 3156.8 - 2858.04 = 298.757
- Frame width at the subject = 35 > 0 ? 3 * 8.8 / 35 : 0 = 0.754 286
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 2/3 inch
| Lens | Full-frame equivalent |
|---|---|
| 12 mm | 47.2 mm |
| 16 mm | 62.9 mm |
| 24 mm | 94.4 mm |
| 35 mm | 137.7 mm |
| 50 mm | 196.7 mm |
| 85 mm | 334.3 mm |
| 135 mm | 531.0 mm |
| 200 mm | 786.7 mm |
Frequently asked
What is the crop factor of a 2/3 inch sensor?
3.933, calculated from its 11.00 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.