The arithmetic
| Quantity | Formula |
|---|---|
| Crop factor | 43.27 mm ÷ sensor diagonal |
| Equivalent focal length | focal length × crop factor |
| Angle of view | 2 · arctan(sensor dimension ÷ 2f) |
| Equivalent aperture (depth of field only) | f-number × crop factor |
43.27 mm is the diagonal of a 36 × 24 mm frame, which became the reference simply because 35 mm film won the twentieth century. Nothing about it is physically special.
What equivalence actually means
The phrase covers three separate claims, and they are not equally true.
Framing — true
A 25 mm lens on Micro Four Thirds frames the same scene as a 50 mm on full frame, from the same spot. This one is pure geometry and never in dispute.
Depth of field — true
To match the framing you moved to a shorter focal length, and depth of field depends heavily on focal length. Same framing, same distance, same f-number, smaller sensor: more depth of field. Multiplying the f-number by the crop factor gives the full-frame aperture that would look the same.
Exposure — false
f/2 is f/2 everywhere. Your meter does not care what sensor is behind the lens, and neither does your shutter speed. The equivalent aperture describes depth of field and total light gathered by the whole sensor — not brightness per pixel, and not exposure.
Equivalence tells you what a picture will look like on a different format. It does not tell you what to dial in. Frame with the equivalent focal length, expose with the real f-number.
Common formats, at a glance
| Format | Sensor | Diagonal | Crop factor | Normal lens |
|---|
The "normal lens" column is the focal length equal to the sensor diagonal — the classic definition of a lens that renders perspective the way the eye expects. On full frame that is 43 mm, which is why 50 mm has always felt slightly long and 35 mm slightly wide.
Common questions
Does a crop sensor make my lens longer?
No. The lens projects the same image circle; the smaller sensor just records a smaller piece of it. The result looks more magnified because you enlarge that smaller piece to the same viewing size.
Should I multiply my aperture by the crop factor when I meter?
No. Only when comparing depth of field or total light between formats. For exposure, use the aperture printed on the lens.
Why is my phone's 24 mm lens actually 6.8 mm?
Because 24 mm is the equivalent, calculated from the tiny sensor's crop factor of roughly 3.5. The real glass has a focal length near 6.8 mm, which is also why phone photos have so much depth of field. Check it in your own files with the EXIF viewer — most phones record both numbers.
Is Super 35 the same as APS-C?
Close enough that lenses are usually shared. Super 35 is about 24.9 × 18.7 mm with a 1.39 crop factor, slightly wider and taller than a stills APS-C frame. Cine lenses cover it; some APS-C stills lenses vignette at the corners of open-gate Super 35.
Does crop factor affect diffraction?
Effectively yes. Because you enlarge a smaller sensor more to reach the same print size, diffraction becomes visible at wider apertures. Full frame tolerates f/16; Micro Four Thirds starts softening around f/8; a phone would be diffraction-limited at f/4 if it could get there.
Related tools
Four real lenses, named honestly.
Lucid switches your iPhone between its actual physical cameras — ultra-wide, main, 2× sensor crop and telephoto — instead of pretending one virtual lens does everything.