In optics, the f-number (sometimes called focal ratio, f-ratio, or relative aperture[1]) of an optical system expresses the diameter of the entrance pupil in terms of the focal length of the lens; in simpler terms, the f-number is the focal length divided by the “effective” aperture diameter. It is a dimensionless number that is a quantitative measure of lens speed, an important concept in photography.

The term stop is sometimes confusing due to its multiple meanings. A stop can be a physical object: an opaque part of an optical system that blocks certain rays. The aperture stop is the aperture that limits the brightness of the image by restricting the input pupil size, while a field stop is a stop intended to cut out light that would be outside the desired field of view and might cause flare or other problems if not stopped.

In photography, stops are also a unit used to quantify ratios of light or exposure, with one stop meaning a factor of two, or one-half. The one-stop unit is also known as the EV (exposure value) unit. On a camera, the f-number is usually adjusted in discrete steps, known as f-stops. Each “stop” is marked with its corresponding f-number, and represents a halving of the light intensity from the previous stop. This corresponds to a decrease of the pupil and aperture diameters by a factor of \sqrt{2} or about 1.414, and hence a halving of the area of the pupil.
A 35 mm lens set to f/11, as indicated by the white dot above the f-stop scale on the aperture ring. This lens has an aperture range of f/2.0 to f/22

Modern lenses use a standard f-stop scale, which is an approximately geometric sequence of numbers that corresponds to the sequence of the powers of the square root of 2: f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, f/45, f/64, f/90, f/128, etc. The values of the ratios are rounded off to these particular conventional numbers, to make them easy to remember and write down.

Shutter speeds are arranged in a similar scale, so that one step in the shutter speed scale corresponds to one stop in the aperture scale. Opening up a lens by one stop allows twice as much light to fall on the film in a given period of time, therefore to have the same exposure at this larger aperture, as at the previous aperture, the shutter speed is set twice as fast (i.e., the shutter is open half as long); the film will usually respond equally to these equal amounts of light, since it has the property known as reciprocity. Alternatively, one could use a film that is half as sensitive to light, with the original shutter speed.

Photographers sometimes express other exposure ratios in terms of ’stops’. Ignoring the f-number markings, the f-stops make a logarithmic scale of exposure intensity. Given this interpretation, one can then think of taking a half-step along this scale, to make an exposure difference of “half a stop”.