How this calculator works
Every sensor captures a rectangle of the image circle, and a smaller rectangle captures a narrower angle from the same lens. The crop factor expresses that as the full-frame diagonal divided by the sensor diagonal. A full-frame sensor has a diagonal of 43.267 mm, so its crop factor is exactly 1. Canon APS-C, with a 22.3 by 14.9 mm sensor, has a diagonal of 26.820 mm and a crop factor of about 1.613. Multiplying a lens focal length by the crop factor gives the full-frame focal length with the same angle of view. The aperture equivalence multiplies as well, because the smaller sensor collects light from a smaller area; the depth of field at the equivalent focal length and f-number then matches.
Formula
crop factor = 43.267 mm / sensor diagonal, where sensor diagonal = sqrt(width^2 + height^2). full-frame equivalent focal length = focal length x teleconverter multiplier x crop factor. full-frame equivalent f-number = f-number x teleconverter multiplier x crop factor.
Worked example
A 50 mm f/1.8 lens on a Canon APS-C sensor (22.3 by 14.9 mm) has a diagonal of 26.820 mm and a crop factor of 1.6132. Its full-frame equivalent focal length is 50 x 1.6132 = 80.66 mm, and its equivalent aperture is 1.8 x 1.6132 = 2.904. The sensor area is 22.3 x 14.9 = 332.27 square millimetres. Adding a 1.4 times teleconverter changes the focal length to 70 mm and the working f-number to 2.52 before the crop conversion, so the full-frame equivalents become 112.93 mm and 4.065.
Advertisement
Frequently asked questions
Does a crop sensor magnify the subject?
No. It records a smaller rectangle of the lens image circle, which looks magnified in the finished picture because you are comparing the whole frame. The true magnification of the subject on the sensor is unchanged.
Why does the equivalent aperture change?
The equivalent f-number preserves the same depth of field and total light across formats. The lens still gathers light at its marked f-number, but the smaller sensor receives less of it overall, and the equivalent figure reflects that.
What is the crop factor of one-inch and micro four thirds sensors?
Micro four thirds is about 2.0 times with a 17.3 by 13 mm sensor, and a one-inch sensor is about 2.7 times with a 13.2 by 8.8 mm sensor. Phone sensors are smaller again and commonly sit between 4 and 8 times.
Do teleconverters and focal reducers change the crop factor?
No, the sensor diagonal sets the crop factor. A teleconverter multiplies the focal length and f-number, while a focal reducer shortens the focal length and lowers the f-number; both effects are applied before the crop conversion here.