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

Question

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.

UPDATE: this formula should look like this

Guide Number = (Shooting Distance * f-number) ÷ ISO factor

See the answer for the details!

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 sqrt(2), 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.

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