How the crop factor is calculated
The crop factor compares a sensor with the 35mm film frame (36 × 24 mm, diagonal 43.3 mm). It is the ratio of the two diagonals. Multiplied by the focal length it gives the 35mm equivalent focal length, multiplied by the f-number the equivalent aperture:
crop factor = 43.27 mm ÷ sensor diagonal
35mm equivalent focal length = focal length × crop factor
equivalent aperture = f-number × crop factor
The Exif standard (CIPA DC-008) defines the 35mm equivalent focal length as the focal length assuming a 35mm film camera and keeps the actual focal length in a separate tag. The lens does not change, only the part of its image that the sensor records. The perspective stays the same, because it depends only on where the camera stands.
Equivalent aperture and depth of field
For the same framing from the same position, a smaller sensor needs a shorter focal length. At the same f-number the aperture opening is then smaller, and the depth of field is greater. For the same depth of field the f-number has to be multiplied by the crop factor as well: f/1.4 on APS-C (crop factor 1.53) gives the depth of field of about f/2.1 on full frame.
The exposure is not converted. f/2 stays f/2 for shutter speed and ISO on every sensor, because the illuminance on the sensor depends only on the f-number. A smaller sensor collects less light in total because its area is smaller, but that is not part of the equivalent aperture shown here.
Sensor formats and crop factors
Typical sizes of common formats with crop factor, the 35mm equivalent of a 50 mm lens and the equivalent of f/2.
| Format | Sensor size | Diagonal | Crop factor | 50 mm equals | f/2 equals |
|---|---|---|---|---|---|
| 1/2.3" | 6.17 × 4.55 mm | 7.67 mm | 5.64× | 282 mm | f/11.3 |
| 1/1.7" | 7.60 × 5.70 mm | 9.50 mm | 4.55× | 228 mm | f/9.1 |
| 1-inch | 13.20 × 8.80 mm | 15.86 mm | 2.73× | 136 mm | f/5.5 |
| Four Thirds / MFT | 17.30 × 13.00 mm | 21.64 mm | 2.00× | 100 mm | f/4 |
| APS-C Canon | 22.30 × 14.80 mm | 26.76 mm | 1.62× | 81 mm | f/3.2 |
| APS-C | 23.50 × 15.60 mm | 28.21 mm | 1.53× | 77 mm | f/3.1 |
| Full frame | 36.00 × 24.00 mm | 43.27 mm | 1.00× | 50 mm | f/2 |
| Medium format 44 × 33 | 43.80 × 32.90 mm | 54.78 mm | 0.79× | 39 mm | f/1.6 |
| Medium format 54 × 40 | 53.40 × 40.00 mm | 66.72 mm | 0.65× | 32 mm | f/1.3 |
The sensor sizes are typical values. They vary a little between camera models and makers, and so does the exact crop factor.
Crop factors of camera systems
The lens pages of this site use these nominal crop factors for the equivalent focal length. They are rounded and differ slightly from the calculated values in the table above, for example 1.5 and 1.6 for APS-C instead of 1.53 and 1.62.
| System | Crop factor |
|---|---|
| Sony E / Nikon Z / Nikon F (APS-C, DX) | 1.5× |
| Fujifilm X | 1.5× |
| Canon RF-S / EF-S | 1.6× |
| Canon EF-M | 1.6× |
| Micro Four Thirds | 2× |
| Fujifilm GFX | 0.79× |
| Hasselblad X | 0.79× |
What to keep in mind
Sensor sizes differ between models, so the crop factor of a particular camera can deviate from the typical value. The data sheet of the camera gives the exact size, which can be entered as an own size. Some cameras use only part of the sensor for video or in crop modes, which changes the crop factor of the recorded image.
A lens made for a smaller format (an APS-C lens) on a full frame body of the same mount works in crop mode: the camera records the area of the smaller format, so the crop factor of that format applies.
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Frequently asked questions
What is the crop factor?
The ratio of the diagonal of the 35mm film frame (43.3 mm) to the diagonal of the sensor. A sensor with a crop factor of 2 has half the diagonal of full frame and records the same angle of view with half the focal length.
Does a crop sensor change the focal length of a lens?
No. A 50 mm lens stays a 50 mm lens. The smaller sensor only records a smaller part of the image, so the angle of view equals that of a longer lens on full frame: 75 mm with a crop factor of 1.5.
What is the equivalent aperture?
The f-number that gives the same depth of field on full frame for the same framing from the same position. It is the f-number multiplied by the crop factor. It says nothing about exposure: the exposure follows the real f-number.
How is a Micro Four Thirds lens converted to full frame?
Focal length and f-number are multiplied by the crop factor of about 2. A 25 mm f/1.8 lens corresponds to 50 mm f/3.6 in angle of view and depth of field.
Why do 1.5 and 1.53 both appear for APS-C?
1.5 is the rounded, nominal crop factor. 1.53 follows from a typical sensor of 23.5 × 15.6 mm. Canon's smaller APS-C sensor gives 1.62, nominally 1.6.
Sources
- CIPA / JEITA: Exif Version 2.3 (CIPA DC-008-2012), tags FocalLength and FocalLengthIn35mmFilm. https://www.cipa.jp/std/documents/e/DC-008-2012_E.pdf