Crop factor and equivalence, without the arguments

Crop factor is one of the few pieces of photographic theory that is simultaneously simple, universally agreed on, and the source of a decade of unresolved internet argument. The simple part is the framing. The argument is about aperture, and it happens because two groups of people are using the same word for different things and neither realises it.

Where the number comes from

A sensor smaller than 35mm film sees a smaller portion of the image a lens projects. How much smaller is described by the crop factor, which is the ratio of the full frame diagonal to the sensor's own diagonal.

Full frame's diagonal is 43.3mm. An APS-C sensor at 23.5 × 15.7mm has a diagonal of 28.2mm, and 43.3 / 28.2 gives 1.53 — the familiar 1.5x. Canon's APS-C is slightly smaller and comes out at 1.6x. Micro Four Thirds lands on 2.0x, which was chosen rather than arrived at.

Note that this is a ratio of diagonals, not areas. A 2x crop factor sensor has a quarter of the area, not half. People routinely reach for the wrong one of those.

The part everyone agrees on

Multiply the focal length by the crop factor and you get the full frame focal length that would frame the same scene from the same position.

A 35mm lens on APS-C frames like a 52mm on full frame. A 25mm on Micro Four Thirds frames like a 50mm. This is why a "nifty fifty" for Micro Four Thirds is a 25mm lens, and why the crop factor is printed on the side of nothing at all and has to be remembered.

Two things it does not mean. The lens's actual focal length has not changed — a 35mm lens is a 35mm lens on any body, and its optical behaviour, its close focus distance and its magnification are all unchanged. And the sensor is not magnifying anything; it is recording a smaller part of a projected circle. "Reach" from a crop sensor is a real practical benefit but it comes from cropping, not from magnification.

The part that starts fights

Now aperture. The claim that begins the argument is that an f/1.8 lens on APS-C is "equivalent to f/2.7" on full frame.

This is true of some things and false of others, and which ones is the whole issue.

It is true of depth of field. Frame the same subject the same size from the same distance, and the smaller sensor with its shorter lens gives more depth of field, by roughly the crop factor. A 35mm f/1.8 on APS-C produces depth of field very close to a 50mm f/2.7 on full frame. If depth of field is what you care about, the multiplication is correct and useful.

It is true of total light captured, and therefore of noise. This is the part people find counterintuitive. The f-number describes light per unit area, and at f/1.8 both sensors receive the same illumination per square millimetre. But the full frame sensor is collecting that illumination over 2.3 times the area, so it gathers 2.3 times as many photons for the same scene and the same shutter speed. Photon shot noise scales with the square root of the signal, so the larger sensor has an inherent signal-to-noise advantage of about a stop and a bit. That is the real, physical basis of "full frame is better in low light", and it has nothing to do with pixel size.

It is false of exposure. This is where the argument goes wrong. Your light meter does not care about sensor size. f/1.8 at 1/100 at ISO 400 is the same exposure on every camera ever made, and a handheld meter reading is valid across formats. The smaller sensor is not two-thirds of a stop darker, and setting f/2.7 on the full frame body to "match" gives you a darker image at the same ISO, not an equivalent one.

So both camps are right. The person saying "f/1.8 is f/1.8" means exposure. The person saying "it's really f/2.7" means depth of field and noise. They are describing the same photograph and could stop arguing at any time.

What actually matters when choosing

Strip out the theory and a few practical consequences remain.

Smaller formats give more depth of field at the same framing and aperture, which is a nuisance for portraits and a genuine advantage for macro and landscape work. At high magnification, depth of field is measured in fractions of a millimetre and any extra is welcome.

Larger formats have a real low-light advantage, worth roughly one stop from full frame to APS-C and two to Micro Four Thirds, all else being equal. All else is frequently not equal — sensor generation matters more than sensor size across a decade of technology.

Smaller formats have smaller, lighter, cheaper lenses for the same field of view and depth of field, and that is not a trick of the maths. Building a full frame equivalent of a Micro Four Thirds system means genuinely larger glass.

And the fast-lens gap is real. Getting full frame f/1.4 depth of field on Micro Four Thirds requires an f/0.7 lens, which does not meaningfully exist. If very shallow depth of field is central to your work, the larger format is not a preference, it is a requirement.

Where crop factor gets misapplied

Teleconverters. A 1.4x converter genuinely changes focal length and genuinely costs a stop of light. Crop factor does neither. They are not the same operation and combining them casually produces nonsense.

Macro magnification. A 1:1 macro lens is 1:1 on any body. The subject fills more of the frame on the smaller sensor because the frame is smaller, so you get more subject magnification in the final image, but the reproduction ratio at the sensor is unchanged. The magnification calculator works in reproduction ratio for this reason.

Diffraction. Smaller sensors hit visible diffraction at wider apertures, because the Airy disc is the same physical size but the sensor and its pixels are smaller. This partly offsets the depth of field advantage of small formats, and is covered in the diffraction limit is not a cliff.

Image stabilisation and shutter speed rules. The old 1/focal-length rule refers to the equivalent focal length, because what matters is angular magnification of the shake in the final image. On APS-C, a 50mm lens wants 1/75s, not 1/50s.

A working summary

Multiply focal length by crop factor to know how it will frame. Multiply the f-number by the same factor when you want to compare depth of field or noise between formats. Never multiply it when you are setting exposure.

If you want the numbers rather than the reasoning, the equivalent focal length calculator does both halves and labels which is which, and the sensor comparison calculator will show you the diagonals the crop factors come from.