f Number Arithmetic

This tab lets you perform arithmetic on "f numbers", also known as "aperture values." Currently, this tab understands two different calculations:

  1. 'f2' as 'f1' plus 'stops': This calculation lets you add an arbitrary number of "f stops" to an arbitrary aperture value. Most SLR users know that f/2.8 plus two stops is f/5.6, but what is f/2.8 plus three and a half stops? (Answer: About f/9.4.)
  2. 'stops' as 'f2' minus 'f1': This calculation lets you find out how far apart two aperture values are, in stops. This is especially useful when comparing variable-aperture zoom lenses, since these often do not use "even" aperture values. For example, Canon makes a 28-105mm f/3.5-4.5 lens. Clearly, f/3.5 is slower than f/2.8, but by how much? (Answer: Roughly two thirds of a stop.)

In the second calculation, you can also choose to have the 'stops' value rounded off to the nearest 1/2 or 1/3 stop. You can turn this feature on in the Rounding Rules dialog.

About f Numbers

f numbers, or aperture values, are a measurement of the size of the hole that the light passes through in the rear of a lens, relative to the focal length of the lens. The smaller the f number, the more light gets through the lens. Each additional "f stop" means that half as much light gets through the lens. So, at f/2, twice as much light gets through the lens as when you set that same lens at f/2.8.

f numbers are a fraction of the focal length of the lens. That is, f/2.8 on a 50mm lens is 1/2.8 of 50mm, or about 18mm in diameter. (This is why you sometimes see f numbers written as a ratio, like 1:2.8.)

The term "stops" comes from the early days of photography, when photographers would place thin wooden panels with holes cut in them between the lens and the film (photographic plates, actually), to "stop" a certain amount of light from reaching the photographic plates.

Formulæ Used

f stops are powers of the square root of two. The first f stop is sqrt(2) to the zeroth power, or f/1.0. Next is sqrt(2) to the first power, or f/1.4, and then sqrt(2) squared for f/2, etc. As you can see, common values like f/2.8 are actually approximations of the unwieldy "true" values. Some versions of f/Calc show you these ugly values when you pick f numbers from its pull-downs, simply because it does its calculations based on the numbers in the fields. (Other versions are smart enough to show you the approximation but use the true value internally.)

  1. To calculate a new aperture value f2 from an initial aperture f1 and a given number of stops, we first convert f1 to a number of f stops from f/1.0, with this formula:

    Then, we add the result of that to stops, and convert back to an aperture value with:

  2. To calculate the number of f stops between f1 and f2, first convert both values to a count of f stops from f/1.0 as above, subtract the results, and convert back to an aperture value.