f Number Arithmetic

The "f Numbers" 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 calulcation 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 very popular 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 1/6 of a stop. Why 1/6? Because both 1/2 and 1/3 stop increments are popular; 1/6 covers both ranges.

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. 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 to the zeroth power, or f/1.0. Next is to the first power, or f/1.4, and then squared for f/2, etc. As you can see, common values like f/2.8 are actually approximations of the unwieldy "true" values.

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.