F-stop Fun Facts

Did you ever wonder how they decided upon camera lens f-stop numbering? Are there any other numbering schemes that could be useful? And did you know that the ‘F’ stands for “focal ratio”, which is “the ratio of the system's focal length to the diameter of the entrance pupil”.

Nikkor Noct f/1.2 (half-stop faster than f/1.4)

F-stops by the numbers

F-stop progression

Did you know that the standard F-stop numbering scheme comes from a math sequence? Most people know that full stops are based upon doubling or halving light intensity, but not where the actual numbering scheme comes from. Now you know.

If you wanted to calculate “standard” F-stop ranges, here’s what you would do:

F-stop full scale calculation

For the above, the progression solving the above sequence would be:

1, 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, 11.0, 16.0 …

You can actually go the other direction, too, if you use (-1 x 0.5), (-2 x 0.5), … for the exponent sequence above! This gets you F-stops like 0.5 and 0.707 for those lenses few mortals will ever be able to afford.

F-stop half-scale calculation

For the above, the progression solving the above sequence would be:

1, 1.2, 1.4, 1.7, 2.0, 2.4, 2.8, …

F-stop third-scale calculation

For the above, the progression solving the above sequence would be:

1, 1.12, 1.26, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, …

If they ever made them, you should now be able to see how lens manufacturers could mark lenses in fourth-stop, fifth-stop, sixth-stop etc. using fractions in the exponents like 4, 5, 6. You’d think that could be useful for something like cinema lenses, where they like finer exposure control, but instead they go one better and offer step-less aperture control.

Speaking of cinema lenses, those lenses are marked in “T” stops, where the T is for “transmission”. I think all lenses should be marked this way, because what really counts is how much light gets to your camera sensor. The F stops can be off by up to a whole F-stops’ worth of transmission, depending upon the lens design and how good the lens multi-coating is. Zoom lenses are particularly dishonest about their transmission.

It doesn’t make you a better photographer, but its fun to know how things got to be the way they are.

By the way, did you know that early camera shutter speeds had sequences like 1/400, 1/200, 1/100, 1/50… ? That actually seems more logical to me than what they have today. Also, did you know that speeds like 15 and 30 seconds are actually 16 and 32 seconds, respectively? The camera makers just lie about these values. Time them for yourself to see.

#howto