How Crop Factor Works
Crop factor (also called focal length multiplier) compares the diagonal of a camera sensor to the diagonal of a traditional 35 mm film frame, which measures 36 x 24 mm and has a diagonal of 43.27 mm. When a sensor is smaller than full frame, it captures only the central portion of the image circle projected by the lens, effectively cropping the image. The crop factor tells you how many times smaller the sensor diagonal is compared to the full-frame standard.
The formula is straightforward:
Sensor diagonal = sqrt(width² + height²)
Crop factor = Full frame diagonal (43.27 mm) / Sensor diagonal
Common Sensor Sizes and Crop Factors
| Sensor Type | Dimensions (mm) | Diagonal (mm) | Crop Factor |
|---|
| Medium Format 645 (Fujifilm GFX) | 43.8 x 32.9 | 54.77 | 0.79x |
| Full Frame (35 mm) | 36 x 24 | 43.27 | 1.0x |
| APS-H (Canon 1D) | 27.9 x 18.6 | 33.53 | 1.29x |
| APS-C (Nikon, Sony, Pentax) | 23.5 x 15.6 | 28.21 | 1.53x |
| APS-C (Canon) | 22.3 x 14.9 | 26.82 | 1.61x |
| Micro Four Thirds | 17.3 x 13.0 | 21.64 | 2.00x |
| 1-inch | 13.2 x 8.8 | 15.86 | 2.73x |
| 1/1.7-inch (compact) | 7.2 x 5.4 | 9.00 | 4.81x |
| 1/2.3-inch (smartphone-class) | 6.17 x 4.55 | 7.67 | 5.64x |
Equivalent Focal Length
To find the field of view equivalent on full frame, multiply your actual focal length by the crop factor:
Equivalent focal length = Actual focal length x Crop factor
For example, a 35 mm lens on an APS-C camera (crop factor 1.53) gives the same field of view as a 53 mm lens on full frame. This is why APS-C shooters often choose a 35 mm lens as their standard lens, whereas full-frame shooters typically use a 50 mm for the equivalent perspective.
Crop Factor and Depth of Field
Crop factor does not change the actual aperture of a lens (which determines light gathering and exposure). However, to achieve the same depth of field as full frame, you need to account for the crop factor in the aperture as well:
Equivalent aperture (for depth of field) = Actual aperture x Crop factor
A 25 mm f/1.4 lens on Micro Four Thirds (crop factor 2.0) is equivalent in field of view to a 50 mm lens, and in depth of field to a 50 mm f/2.8 on full frame. To match full-frame background blur with an equivalent lens, you need to open up proportionally wider on the cropped sensor.
Worked Example
A Nikon APS-C sensor measures 23.5 x 15.6 mm. Its diagonal is sqrt(23.5² + 15.6²) = sqrt(552.25 + 243.36) = sqrt(795.61) = 28.20 mm. The full-frame reference diagonal is sqrt(36² + 24²) = 43.27 mm. The crop factor is 43.27 / 28.20 = 1.53x. A 50 mm f/1.8 lens on this camera gives an equivalent focal length of 50 x 1.53 = 76.7 mm (rounded to 77 mm), and an equivalent depth-of-field aperture of f/1.8 x 1.53 = f/2.8 compared to a full-frame camera. These are the default values shown by the calculator above.
Related Calculators
Sources and method: Crop factor formula derived from the ISO 1007:1976 standard 35 mm film frame size (36 x 24 mm). Sensor dimensions from manufacturer specifications (Nikon, Canon, Sony, Olympus/Panasonic, Fujifilm). Diagonal calculated using the Pythagorean theorem: d = sqrt(w² + h²).
Sensor dimensions vary slightly between manufacturers and individual camera models. Crop factor figures are approximations based on nominal sensor sizes. Check your camera's official specifications for exact dimensions.
