Crop factor is a framing conversion, not a change in the lens
A lens has one focal length and it never changes. What changes between cameras is how much of the image circle the sensor collects. A smaller sensor takes a smaller rectangle out of the same projected image, so the picture is a tighter view of the same scene — the crop in crop factor.
To express that tighter view as a number people can use, the industry compares it with 35 mm film, whose 36 × 24 mm frame has a diagonal of 43.27 mm. Divide that reference diagonal by your sensor's diagonal and you have the crop factor: 1.53 for a 23.5 × 15.6 mm APS-C sensor, 2.0 for Micro Four Thirds, 2.7 for a 1-inch type, 0.79 for a 44 × 33 mm medium format back. Multiply your lens's focal length by that factor and you get the full-frame focal length that would frame the same scene from the same spot.
Two things do not happen when you mount a lens on a smaller sensor. The lens does not become longer — perspective, compression and the relationship between subject and background depend on where you stand, not on the sensor. And the lens does not become slower in exposure terms: f/2.8 meters as f/2.8 on every format, because the f-number describes illuminance per unit area and the area does not care how big the sensor is.
The three equivalences, and which of them are real
Focal length equivalence is uncontroversial. Multiply by the crop factor and you get the same framing. A 35 mm lens on a 1.53× APS-C camera frames like a 54 mm lens on full frame — which is why 35 mm has become the standard "normal" prime for APS-C.
Aperture equivalence is real but easily misread. Multiply the f-number by the crop factor and you get the full-frame f-number that produces the same depth of field and collects the same total light. Both follow from the physical aperture diameter: f/1.8 on a 25 mm lens is an opening 13.9 mm across, while f/1.8 on a 50 mm lens is 27.8 mm across, and the bigger opening gathers four times the light and blurs the background far more. So a 25 mm f/1.8 on Micro Four Thirds gives the depth of field and total light of a 50 mm f/3.6 on full frame. It does not give an f/3.6 exposure — the exposure is f/1.8, because the same light is concentrated onto a quarter of the area.
ISO equivalence follows from the same logic. Because the small sensor collects one-quarter of the total light for the same exposure settings, matching the noise performance of a full-frame image would require the full-frame camera to work at crop² times the ISO. That is the sense in which base-ISO images from larger sensors look cleaner: they have collected more photons, and photon shot noise scales with the square root of the count.
What none of these equivalences capture is lens character, sensor generation, colour filter array design or read noise. Two cameras with the same equivalent settings can still look different, and a modern small sensor frequently beats an older large one.
Worked example: a 25 mm f/1.8 on Micro Four Thirds
You are choosing between a Micro Four Thirds body with a 25 mm f/1.8 and a full-frame body, and want to know what lens you would need on full frame to match.
- Sensor diagonal. √(17.3² + 13.0²) = √(299.29 + 169) = √468.29 = 21.640 mm.
- Reference diagonal. √(36² + 24²) = √(1,296 + 576) = √1,872 = 43.267 mm.
- Crop factor. 43.267 ÷ 21.640 = 1.9994, which is why Micro Four Thirds is quoted as exactly 2×.
- Equivalent focal length. 25 × 1.9994 = 50.0 mm.
- Equivalent aperture. 1.8 × 1.9994 = f/3.60 for depth of field and total light.
- Equivalent ISO. 400 × 1.9994² = ISO 1,599 — call it 1,600.
- Angle of view. 2 × arctan(17.3 ÷ 50) = 2 × 19.09° = 38.2° horizontally, against 39.6° for a 50 mm on full frame. The small difference exists because Micro Four Thirds is 4:3 and full frame is 3:2, so matching diagonals cannot match both axes.
The practical reading: this combination gives you a normal lens with moderate subject separation, in a body and lens far smaller and lighter than the full-frame equivalent. Whether that trade is worth it depends on whether you needed f/1.8 depth of field or f/1.8 light.
Using the numbers when you buy
For framing, compare equivalent focal lengths. If you know you like 35 mm on full frame, you want roughly 23 mm on APS-C and 17 mm on Micro Four Thirds. Buying by the marked focal length across systems is how people end up with three lenses that all frame the same way.
For background blur and low light, compare equivalent apertures. An f/2.8 zoom on APS-C behaves like an f/4.3 zoom on full frame. That is the honest comparison when a manufacturer advertises a "fast" small-format zoom, and it is also why f/1.2 and f/1.4 primes exist for smaller formats: they are how those systems reach full-frame f/2 rendering.
For reach, the crop factor is genuinely useful. Putting a 300 mm lens on a 2× body gives 600 mm framing at the weight of a 300 mm lens. You are not getting extra magnification for free — you are simply cropping — but if your sensor has enough pixels on the subject, the result is the same as cropping a larger image, with a smaller file and a faster burst rate.
Watch the aspect ratio. The crop factor matches diagonals. Full frame and APS-C are both 3:2, so their horizontal and vertical fields match too. Micro Four Thirds is 4:3 and medium format 44 × 33 is also 4:3, so converting between 3:2 and 4:3 gives a slightly wider vertical and slightly narrower horizontal view than the single number implies. The angle-of-view output is the number to trust when framing precision matters.
Once you have settled the format, the depth of field calculator and the hyperfocal distance calculator use the same sensor diagonal to derive the circle of confusion, and the print size and DPI calculator tells you how large the resulting file will print.
Sensor formats, diagonals and crop factors
| Format | Dimensions (mm) | Diagonal (mm) | Crop factor | 24 mm frames like | 50 mm frames like |
|---|---|---|---|---|---|
| Medium format 53.4 × 40 | 53.4 × 40.0 | 66.72 | 0.649 | 15.6 mm | 32.4 mm |
| Medium format 44 × 33 | 44.0 × 33.0 | 55.00 | 0.787 | 18.9 mm | 39.3 mm |
| Full frame 35 mm | 36.0 × 24.0 | 43.27 | 1.000 | 24.0 mm | 50.0 mm |
| APS-H | 28.7 × 19.0 | 34.42 | 1.257 | 30.2 mm | 62.9 mm |
| Super 35 cine | 24.89 × 18.66 | 31.11 | 1.391 | 33.4 mm | 69.5 mm |
| APS-C (Sony, Nikon, Fuji) | 23.5 × 15.6 | 28.21 | 1.534 | 36.8 mm | 76.7 mm |
| APS-C (Canon) | 22.3 × 14.9 | 26.82 | 1.613 | 38.7 mm | 80.7 mm |
| Micro Four Thirds | 17.3 × 13.0 | 21.64 | 1.999 | 48.0 mm | 100.0 mm |
| 1 inch type | 13.2 × 8.8 | 15.86 | 2.727 | 65.5 mm | 136.4 mm |
| 1/2.3 inch type | 6.17 × 4.55 | 7.67 | 5.644 | 135.5 mm | 282.2 mm |
Dimensions are the nominal active areas; individual cameras differ by a few tenths of a millimetre, which moves the crop factor in the third decimal place only.
"1 inch" sensors are not one inch across
The inch-type designations are inherited from 1950s video camera tubes, where the number described the outside diameter of the glass envelope rather than the imaging area. A "1 inch type" sensor measures 13.2 × 8.8 mm with a 15.86 mm diagonal — about two thirds of an inch. A "1/2.3 inch type" is 7.66 mm across the diagonal. Treat those names as product categories, and take the millimetre dimensions from the specification sheet whenever the exact number matters.
Misunderstandings worth clearing up
- A crop sensor does not magnify. It records a smaller part of the same projected image. Perspective is set by camera position alone.
- Equivalent aperture is not exposure. f/2.8 exposes as f/2.8 on every format. The equivalent number describes depth of field and total light collected.
- Lens focal lengths are never marked as equivalents on interchangeable-lens cameras. A 23 mm APS-C lens is a real 23 mm lens; compact cameras, by contrast, usually advertise the equivalent.
- Crop factor does not change the maximum aperture you can buy. It changes what that aperture does, which is why small formats need faster glass for the same rendering.
- Rounded factors hide real differences. Canon APS-C at 1.61 and Sony APS-C at 1.53 differ by 5%, which is visible when you are matching two cameras on a shoot.
- Diagonal matching is not axis matching. Between 3:2 and 4:3 formats the horizontal and vertical fields shift in opposite directions.
Where the 35 mm reference came from, and other equivalences
The 36 × 24 mm frame is a historical accident that became a standard. It was created by running perforated 35 mm cine film horizontally through a still camera, giving a frame double the width of the cine frame, and it became so dominant through the twentieth century that photographers learned focal lengths in its terms. Digital sensors were initially smaller than that frame for cost reasons, and the crop factor was invented as a translation layer for photographers who already thought in 35 mm.
Two related equivalences use the same reasoning. Diffraction scales with the f-number, so a small sensor reaches its diffraction limit at a wider aperture: if full frame starts softening around f/11, a Micro Four Thirds camera does so around f/5.6, which is exactly the equivalent aperture relation applied to resolution. Circle of confusion, the blur spot considered acceptably sharp, is conventionally taken as the sensor diagonal divided by about 1,500, so it too scales with format — which is why depth-of-field tables are format-specific and why the depth of field calculators on this site ask which sensor you are using.
For video the reference shifts. Cinema has its own history, and Super 35 — the format most cine lenses were designed for — sits at a 1.39× factor against 35 mm stills. A cinematographer describing a lens as "wide" is usually thinking in Super 35 terms, which is a different mental scale from a stills photographer's.
The honest summary: crop factor is a translation tool for people who already have an intuition in one format. If you learn a system on its own terms — knowing what 12 mm, 25 mm and 45 mm do on your camera — you never need it at all, except when comparing gear with someone who learned on a different system.