How Is a Lens f-Number Affected by Crop Factor?
Crop factor doesn’t actually change the physical f-number of a lens, but it absolutely changes how that f-number behaves in practice, and that’s where people get tripped up a bit.
The f-number itself is purely optical. It’s defined as the focal length divided by the diameter of the entrance pupil. So if you mount a 50mm f/2 lens on a full-frame camera and then mount that exact same lens on an APS-C body, it is still a 50mm f/2 lens. The physical aperture size does not change. The amount of light per unit area hitting the sensor also does not change. In terms of exposure settings — shutter speed, ISO, and f-number — nothing changes because of crop factor. An f/2 exposure is an f/2 exposure.
Where crop factor enters the picture is field of view and depth of field. A smaller sensor captures a smaller portion of the image circle, so the framing becomes tighter. A 50mm lens on a 1.6× APS-C body gives the same field of view as an 80mm lens on full frame. That’s straightforward.
Now here’s the subtle but important part: if you want the same framing and the same perspective on both formats, you would use a shorter focal length on the smaller sensor. For example, instead of 50mm on full frame, you might use around 31mm on a 1.6× crop body to get the same composition. And when you do that, depth of field changes.
To compare depth of field equivalently across formats, you multiply the f-number by the crop factor. So:
Equivalent f-number (for depth of field) = f-number × crop factor.
Example: Full frame: 50mm at f/2 APS-C (1.6×): 31mm at f/2
The APS-C setup will have deeper depth of field. To get similar background blur to full frame at f/2, you’d need roughly f/1.2–f/1.3 on APS-C (because 2 ÷ 1.6 ≈ 1.25). That’s why full frame tends to produce shallower depth of field more easily — not because the f-number “changes,” but because achieving equivalent framing requires different focal lengths.
There’s also a light gathering nuance. Total light collected by the sensor depends on sensor size. Even though f/2 gives the same light intensity per unit area, a larger sensor collects more total light overall, which can translate into better signal-to-noise ratio. That’s one reason your Canon R8 or R5 (full frame) will look cleaner at high ISO compared to something like the R100 (APS-C), even if both are set to f/2.
So to summarize in a clean way:
The f-number does not change with crop factor. Exposure does not change. But for equivalent framing, depth of field scales with crop factor. Equivalent depth-of-field f-number = actual f-number × crop factor.
That distinction — exposure vs equivalence — is really the heart of it. Most confusion comes from mixing those two ideas together.