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# Aperture numbers

Anwendung:Background knowledge

Background knowledge on aperture numbers, short and easy to read: Where do the numerical values 4, 5.6, 8, 11 etc. come from? Why do smaller numbers mean a larger aperture? And why is there often an f next to the aperture number?

## Where does the aperture numbers come from?

The aperture number or f-number is the ratio of the focal length and the diameter of the lens opening. An f-number of 4 means that the lens opening is a quarter of the focal length, 8 is an eighth – i.e. less.

Hence: larger f-number → smaller aperture and vice versa.

And therefore the f-number is a pure number without a unit, it is the ratio of two lengths.

It is also called f-stop or aperture number, both mean the same.

## Notation of the aperture number

Strictly speaking "f8" means that the diameter of the aperture is one eighth of the focal length, hence the correct notation for it is f8, a fraction. The letter f originates from "focal length" and is the common symbol for it in physics. It is common to simplify it to "f8", which is how many cameras display it, see the number in the top right corner of the camera display.

## F-stop values

The series of aperture numbers results from the rule that a change of one f-stop should allow twice or half the amount of light to pass through.

The aperture is approximately round and in the case of a circle the area increases quadratically with the diameter: double the diameter → four times the area.

The diameter only has to increase by a factor of about 1.4 for the area to double. (Precisely it would be by the factor √2=1.4142...)

That is why there is a factor of 1.4 between each of the aperture numbers plus some rounding. Every second number – which is supposed to bring a quadrupling of the amount of light – is a doubling with the powers of two: 2 – 4 – 8 – 16.