Aperture is just funky. Well, if you sit around with friends calculating the area of a circle and talk about the next digit of π, then maybe you are just a different kind of normal and aperture is your cup of tea. For the rest of us, though, I highly suggest a time honored method to understanding your camera, though understanding why the numbers are weird will elude you: memorize.
Any of us can calculate that ISO 200 is twice as sensitive as ISO 100, and ISO 400 is twice as fast as as ISO 200. With film sensitivity, a stop of light is easy to figure. Even with the shutter speed, though they inconveniently do not use exact numbers, the key numbers are approximately exponential: 2, 4, 8, 15, 30, 60, 125, 250, 500, 1000. There is a little funny business going on in there, but basically, it is easy to figure a stop of light. Aperture, though? Not so much.
Just like the film sensitivity (ISO) and shutter speed, the aperture is made to help us figure our stops of light, whether cutting the light in half one way or doubling light the other way. Obviously, when you make the aperture smaller, it allows less light, when you make it bigger, it allows more light. Well, the reason the aperture numbers are so awkward is that they are based on the area of a circle, precisely the area of your aperture. And since that calculation includes π and a simple equation, the numbers do not change as simply as multiplying or dividing by two.
So, without further adieu, here are the aperture stops, each number one stop of light less (each number indicating a halving of the light): 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, and that is what you commonly see on lenses. All the other strange decimaled numbers you encounter are simply 1/2 or 1/3 stops between those. You can, of course, do the math, but unless you are pretty savvy calculating π in the head, which is only to prove the concept anyway, you will most likely still end up memorizing that list if your aim is to use it in real life photography.
So, there is my tip for the day, gleaned from the technique course I am about to finish up in a couple days. This may seem like another overly technical piece, but I assure you, it is fiercely practical. If you memorize that list, and think a bit more about the shutter speed and film sensitivity (ISO), you hold the keys of knowledge to unlock every camera ever made, from the thousand-buttoned sport-shooters-delight of the sidelines to the wooden box with polished silver plates.
…that’s what it’s all about! [ clap, clap ]