F-number Equivalence

Given a lens described by an f-number, its effect on Exposure is the same no matter the sensor size of the camera. That’s why f-number is useful in the first place: to reduce the Focal Length and Aperture diameter combination into a single variable that completely describes the lens influence on Exposure.

However, different sensor sizes will play a role on the Depth of Field. After adjusting for Focal Length Equivalence (choosing a focal length that yields equivalent framing and perspective), the depth of field is then determined by the Aperture diameter.

This means that when comparing a camera with a regular sensor (e.g. a full frame DSLR) and another with with a smaller sensor (e.g. a smartphone), it’s impossible to define a perfect equivalence between f-numbers. The same f-number will yield the same Exposure but a different Depth of Field, meanwhile with equivalent focal lengths the same Aperture diameter will yield a different Exposure but the same Depth of Field.

In practice, we’re mostly concerned with comparing lenses by their Depth of Field, given that the Exposure can be controlled through other means. In this scenario, it’s interesting to answer the question: what f-number in a regular camera would provide the same Depth of Field as does this lens with this sensor? This is why f-number equivalence as a concept is a thing, even though it can be misleading because it’s not really equivalent in every way.