The crop factor is one of those numbers every camera owner eventually needs but few online tools handle cleanly. This calculator takes your sensor dimensions and a native lens specification and instantly returns the crop factor, 35 mm equivalent focal length, equivalent aperture for a matched depth of field, and horizontal field of view — all with a step-by-step working panel so you can see exactly where each number comes from.
Why crop factor matters
Every interchangeable-lens camera system — APS-C DSLRs, Micro Four Thirds mirrorless bodies, medium-format cameras — uses a sensor that is either smaller or larger than the 35 mm full-frame standard (36 x 24 mm). A lens projects a circular image onto the sensor; a smaller sensor captures only the centre of that circle, effectively “cropping” it and narrowing the field of view. The crop factor quantifies exactly how much narrower.
Understanding crop factor lets you:
- Buy the right lens. A 35 mm prime on an APS-C body frames like a 53 mm on full frame — close to the classic “nifty fifty” portrait focal length on that system.
- Compare depth of field across systems. An f/1.8 lens on a 2x crop body gives roughly the same depth of field as f/3.6 on full frame, not f/1.8 — a common source of confusion.
- Understand field of view. Wildlife and sports photographers often favour APS-C for its “reach”: the same 400 mm super-telephoto frames like 640 mm on a 1.6x Canon crop body.
How it works
Sensor diagonal is calculated with the Pythagorean theorem:
diag = sqrt(width squared + height squared)
Crop factor is the ratio of the full-frame diagonal to your sensor’s diagonal:
CF = 43.267 mm / sensor_diag
The constant 43.267 mm is the exact diagonal of a 36 x 24 mm full-frame sensor.
Equivalent focal length is the native focal length scaled up by the crop factor — it tells you which full-frame focal length produces an identical field of view:
EFL = native_focal x CF
Equivalent aperture (depth-of-field equivalence only) scales the f-number by the same factor. Depth of field is governed by the physical diameter of the aperture entrance pupil (focal length / f-number). To match full-frame depth of field you need the same entrance-pupil diameter, which on a smaller sensor means the aperture must open by one factor of CF:
Eq. f/ = native_f/ x CF
Horizontal field of view uses the standard pinhole/thin-lens formula, in degrees:
HFoV = 2 x arctan(sensor_width / (2 x focal_length))
Worked example — Canon APS-C with a 24 mm f/2.8 lens
Sensor: 22.2 x 14.8 mm. Diagonal = sqrt(22.2 squared + 14.8 squared) = sqrt(492.84 + 219.04) = sqrt(711.88) approximately 26.68 mm. Crop factor = 43.267 / 26.68 approximately 1.62x.
Equivalent focal length = 24 x 1.62 approximately 38.9 mm (close to the classic 40 mm “street” focal length on full frame).
Equivalent aperture = f/2.8 x 1.62 approximately f/4.5 (the depth of field you see on this APS-C body at f/2.8 matches what full frame gives at f/4.5).
Horizontal FoV = 2 x arctan(22.2 / 48) = 2 x arctan(0.4625) approximately 2 x 24.8 degrees = 49.6 degrees.
| Sensor | Native focal | CF | Equivalent focal | Eq. aperture |
|---|---|---|---|---|
| Full Frame (36 x 24 mm) | 50 mm f/1.8 | 1.00x | 50 mm | f/1.8 |
| APS-C Canon (22.2 x 14.8 mm) | 35 mm f/1.8 | 1.62x | 56.7 mm | f/2.9 |
| APS-C Nikon/Sony (23.5 x 15.6 mm) | 35 mm f/1.8 | 1.52x | 53.2 mm | f/2.7 |
| Micro Four Thirds (17.3 x 13 mm) | 25 mm f/1.4 | 2.00x | 50.0 mm | f/2.8 |
| 1-inch (13.2 x 8.8 mm) | 18.5 mm f/2.8 | 2.72x | 50.3 mm | f/7.6 |
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