In photography there’s something known as the standard f-number series. It’s a geometric sequence of f-numbers that goes like this:
At first this may look like a random series of numbers, but there’s actually a method to this madness, and memorizing this series can help you make quick adjustments to exposure when switching between f-numbers.
What makes this series so special?
The f-numbers in this geometric series are known as whole stops. And, the thing that makes them special is that each number in the series transmits exactly twice or one-half the amount of light of the neighboring f-number.
For example, f/5.6 transmits exactly twice as much light as f/8. This means that if you’re shooting at f/5.6 and want to switch to f/8, but still keep the same exposure, then you’ll have to make your shutter speed exactly two times slower (because at f/8 you’ll be transmitting two times less light). If you were shooting 1/100 sec at f/5.6, then at f/8 you should shoot at 1/50 sec.
Having this f-number series memorized will allow you to switch between f-numbers and quickly calculate the new exposure.
Your camera probably also has intermediate f-numbers between these whole stops (usually in increments of one-half or one-third stops). So, memorizing the whole stop sequence will also help you calculate the exposures for these intermediate stops when switching between f-numbers.
Where do those strange numbers come from, anyway?
The f-numbers are calculated as a ratio between focal length and aperture diameter:
f-number = (focal length) / (aperture diameter)
For example, if you’re shooting with a 100mm lens (the focal length), and the aperture diameter is set to 25mm, then the f-number will be 4 (100/25).
At first you might think that doubling the aperture diameter would allow twice as much light to be transmitted, but it doesn’t work this way because doubling the aperture diameter would more than double the surface area of the aperture.
It’s the surface area that needs to double when you want to transmit twice as much light, and to double the surface area of a circle, you have to multiply its diameter by the square root of 2 (which is about 1.414). And, this is why the whole stops are incremented by a factor of 1.414.
2.8 = 2.0 * 1.414
4 = 2.8 * 1.414
5.6 = 4 * 1.414
…and so on…
I realize this is probably the first time I’ve brought up math in a post, so let me know if any of this makes no sense, and I’ll be happy to clarify as much as I can in the comments 🙂
If you enjoyed this article, and would like to read more, please signup for free updates by email or RSS.
About the Author: Steve Berardi is a naturalist, photographer, computer scientist, and founder of PhotoNaturalist. You can usually find him hiking in the beautiful mountains and deserts of Southern California.