Originally Posted by marko
(Aperture numbers (the F-stop or the hole) can be confusing to newbies UNTIL you think of them as FRACTIONS. F-4 is a larger hole than F-5.6 Just think of it as a fraction and it makes perfect sense. Would you rather have 1/4th of a pie or an 1/5.6th of a pie? A 1/4 is the larger piece. F-5.6 is a larger hole.)
It's actually easier to remember (and understand, I think) if you write the aperture properly, AS a fraction - ie. f/4, f/5.6, etc. The reason it's written this way is that the diameter of the aperture IS a fraction of the focal length (commonly represented by "f").
Therefore, if your focal length (f) is 100mm, at f/4, your "effective" aperture diameter is 100/4, or 25mm. At f/5.6, the aperture diameter is 100/5.6, or about 17.86mm. If you go to f=200mm, at f/4, your aperture is then 200/4, or 50mm. And so on.
An interesting thing to remember as well: every two "stops" is a doubling or halving of the ratio: f/8 is two stops smaller than f/4, and f/2 is two stops larger. Going down two stops from f/5.6 gives you f/11 (rounded off); two stops up is f/2.8. And so on.
The math makes even more sense if you extend this: at 100mm and f/4, for example, you have an aperture diameter of 25mm, or a radius of 12.5mm. Calculating for the area of a circle (pi*r^2), your aperture area is then 490.875mm^2.
Go down one stop to f/5.6, and you get a diameter of 17.86mm, radius of 8.93... and an area of 250.446mm^2... or very close to half the area = half the light allowed through (numbers are all rounded, BTW, including pi - if you don't round things off it's a lot closer to exactly half).
One more stop, to f/8, and the area works out to 122.718mm^2 (rounded off), which is even closer to exactly 1/4 the area of the f/4 aperture.