What is the quantative relation between flash guide number and ISO?

I found that formula on the Internet:

Guide Number = (Shooting Distance * Aperture) ÷ ISO Sensitivity

Is it correct? If it is could someone please explain why ISO is related to guide number in this way. The formula in wikipedia article about guide number does not have ISO in it so I wanted to know if the one I found is the right one and why.

Answer

The formula you've given is incorrect, at least for "straight" values of ISO numbers. ISO is related to sensitivity in that each stop in increased ISO is the same as a single stop of increased aperture. That means that to get ISO 200 guide numbers from ISO 100 numbers, you multiply by the square root of two, just as increasing aperture by that factor is one stop. Quadrupling the ISO doubles the guide number, and so on. Or, expressed the other way around in the equation, as in your formula: the guide number required for a given aperture and distance goes down by a factor of about 1.4 for every stop of increased ISO.

So, it works if you replace "ISO sensitivity" in your formula with something like "ISO factor", where:

ISO  100 = 1
ISO  200 = 1.4
ISO  400 = 2
ISO  800 = 2.8

ISO 1600 = 4
...

Note the familiar sequence of numbers — that's no coincidence.

Then, the final formula would be:

   Guide Number = Shooting Distance × f-number ÷ ISO factor

This formula tells you what GN you'll need from your flash at that distance and with those settings. You can also rearrange the terms; for example, if you have a basic flash with a fixed guide number, and your subject distance is also fixed, you might want to put those terms on the same side, so you can just calculate some number on that side:

   f-number ÷ ISO factor = Guide number ÷ Shooting Distance

For example, if your flash is GN 24m, and your subject is 3 meters away, your magic number is 8 — so, f/8 at ISO 100, or f/11 at ISO 200. Since guide number and distance are "setting up the lights" operations while aperture and ISO are on the camera, I find this an intuitive way to think about it.

Also be aware that halving flash power decreases guide number by, again, a factor sqrt(2). So, if your flash in my example above has the typical fractional power adjustment, and you set it to 1/4 power, the GN becomes 12m, so f/4 at ISO 100.