APS-C crop factor and field of view calculator
A APS-C sensor measures 23.5 by 15.6 mm, a diagonal of 28.21 mm. Against the full-frame diagonal of 43.27 mm that is a crop factor of 1.534. Sony, Nikon, Fujifilm and Pentax all use approximately this size.
The diagonal divided by this gives the acceptable blur circle. 1500 is the usual modern figure.
- Full-frame equivalent focal length
- 53.69
- Equivalent aperture for depth of field
- 4.295
- Sensor diagonal
- 28.207
- Sensor area
- 366.60 mm2
- Full frame gathers this many times more light
- 2.357
- Horizontal field of view
- 37.115 degrees
- Vertical field of view
- 25.127 degrees
- Diagonal field of view
- 43.894 degrees
- Hyperfocal distance
- 23 301
- Depth of field
- 776
- Frame width at the subject
- 2.014
Show the working
- Focal length = 35
- Aperture f-number = 2.8
- Subject distance = 3
- Circle of confusion divisor = 1500
- sensor_w = 23.5 = 23.5
- sensor_h = 15.6 = 15.6
- Sensor diagonal = hypot(23.5, 15.6) = 28.2066
- Crop factor = 28.2066 > 0 ? 43.266615305567875 / 28.2066 : 0 = 1.533 92
- Full-frame equivalent focal length = 35 * 1.533 92 = 53.6872
- Equivalent aperture for depth of field = 2.8 * 1.533 92 = 4.294 98
- Sensor area = 23.5 * 15.6 = 366.6
- Full frame gathers this many times more light = 366.6 > 0 ? 864 / 366.6 : 0 = 2.356 79
- Horizontal field of view = deg(2 * atan(23.5 / (2 * 35))) = 37.1153
- Vertical field of view = deg(2 * atan(15.6 / (2 * 35))) = 25.1269
- Diagonal field of view = deg(2 * atan(28.2066 / (2 * 35))) = 43.894
- coc = 28.2066 / 1500 = 0.018 804 4
- Hyperfocal distance = 35^2 / (2.8 * 0.018 804 4) + 35 = 23 300.9
- near = 3*1000 * 23 300.9 / (23 300.9 + (3*1000 - 35)) = 2661.35
- far = 3*1000 < 23 300.9 ? 3*1000 * 23 300.9 / (23 300.9 - (3*1000 - 35)) : 1e9 = 3437.4
- Depth of field = 3437.4 >= 1e9 ? 1e9 : 3437.4 - 2661.35 = 776.057
- Frame width at the subject = 35 > 0 ? 3 * 23.5 / 35 : 0 = 2.014 29
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.
Sony, Nikon, Fujifilm and Pentax all use approximately this size.
Equivalent focal lengths on APS-C
| Lens | Full-frame equivalent |
|---|---|
| 12 mm | 18.4 mm |
| 16 mm | 24.5 mm |
| 24 mm | 36.8 mm |
| 35 mm | 53.7 mm |
| 50 mm | 76.7 mm |
| 85 mm | 130.4 mm |
| 135 mm | 207.1 mm |
| 200 mm | 306.8 mm |
Frequently asked
What is the crop factor of a APS-C sensor?
1.534, calculated from its 28.21 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.