Crop Factor Calculator

Crop factor is the ratio of the 43.3 mm diagonal of a 36 by 24 mm full-frame image area to the diagonal of the sensor actually in the camera. A lens has a fixed focal length regardless of what sits behind it; what changes is how much of the projected image circle the sensor records. Multiplying the true focal length by the crop factor gives the full-frame focal length that would frame the same scene, which is why a 50 mm lens on a 1.5x body is described as a 75 mm equivalent. The diagonal angle of view follows from 2 arctan(d / 2f), so that 50 mm lens narrows from about 46 degrees on full frame to roughly 31 degrees on APS-C. Standard factors are 1.0x for full frame, 1.5x for Nikon DX, Sony E APS-C and Fujifilm X at about 23.5 by 15.6 mm, 1.6x for Canon APS-C at about 22.3 by 14.9 mm, 2.0x for Micro Four Thirds at 17.3 by 13 mm, 2.7x for a 1-inch sensor, and roughly 0.79x for 44 by 33 mm digital medium format. The common error is treating crop factor as a free telephoto extender. Framing changes but the lens still projects the same image and gathers the same light per unit area, so exposure is unaffected and the f-number does not change. Depth of field does change for equal framing: to match the background blur of a full-frame shot, multiply the f-number by the crop factor, so 50 mm f/1.8 on a 1.5x body renders roughly like 75 mm f/2.7. Manufacturers also round their factors, so treat equivalents as approximate to within a few percent.

The 36 by 24 mm frame that anchors the whole system was not chosen as a standard. Oskar Barnack, working at Ernst Leitz in Wetzlar, built a compact camera around 35 mm perforated cine film in the 1910s and doubled the cine frame to give a wider negative; the Leica production model went on sale in 1925 and the format became so dominant that it was later codified as ISO 1007 under the name 135. For most of the twentieth century almost every 35 mm camera shared it, so lens focal lengths and their angles of view were learned as fixed pairs, with 28 mm meaning wide, 50 mm meaning normal and 135 mm meaning portrait telephoto. Smaller capture areas made the comparison necessary. The Advanced Photo System, introduced in 1996 by a consortium including Kodak, Fujifilm and Canon, used a smaller negative and gave APS-C its name. Early digital SLRs then reached the market with sensors far smaller than full frame because large silicon dies were expensive; the Nikon D1 of 1999 used an approximately 23.7 by 15.6 mm sensor, and photographers needed a conversion to reuse their existing focal-length intuition, so the crop factor multiplier entered common usage. Olympus and Kodak announced the Four Thirds standard in 2003 and the mirrorless Micro Four Thirds derivative followed in 2008, both with a 2.0x factor, and full-frame digital bodies from Canon and later Nikon and Sony kept 1.0x as the reference point.