I found that formula on the Internet:
$$ \text{Guide Number} = \frac{\text{Shooting Distance}\times\text{Aperture}}{\text{ISO Sensitivity}} $$
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.
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 sensitivity | ISO factor |
|---|---|
| 100 | 1 |
| 200 | 1.4 |
| 400 | 2 |
| 800 | 2.8 |
| 1600 | 4 |
| ... | ... |
Note the familiar sequence of numbers — that's no coincidence.
Then, the final formula would be:
$$ \text{Guide Number} = \frac{\text{Shooting Distance} \times \text{f-number}}{\text{ISO factor}} $$
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:
$$ {\text{f-number} \over \text{ISO factor}} = {\text{Guide Number} \over \text{Shooting Distance}} $$
For example, if your flash is GN 24 m, 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 ¼ power, the GN becomes 12 m, so f/4 at ISO 100.
The original post is asking for a quantitative relationship, not a series of examples. There is nothing wrong about the basic guide number relationships used in the above answers, but the quantitative relationship between Guide Number and ISO is
$$ GN \propto \sqrt{\text{ISO}\over 100}\,.$$
In keeping with the use of a series of examples:
$$\begin{align} \sqrt{200\,/100} &= 1.4 \\ \sqrt{400\,/100} &= 2 \\ \sqrt{800\,/100} &= 2.8 \\ & \dots \end{align}$$
The original asker may have wanted this quantitative relationship because his/her camera has ISO values other than 100, 200, 400, 800 etc.
There is a derivation of this relationship at:
The formula you found with ISO included is wrong.
The correct formula is any one of the following equivalent formulas:
$$\begin{align} \text{Guide Number} &= \text{Distance}\times \text{Aperture} \\ \text{Distance} &= \frac{\text{Guide Number}}{\text{Aperture}} \\ \text{Aperture} &= \frac{\text{Guide Number}}{\text{Distance}} \end{align}$$
As you would know, Guide Number is given for ISO 100 always. We will deal with other ISOs a little later.
As a photographer, my first worry would be how far my flash light will be able to fire. If my flash has a rated GN of 40 metres, for ease of calculation we can know that at 10 metres I would need an aperture of f/4. GN/Distance = Aperture. If my subject is at 5 metres, I can shoot at an aperture of f/8 (40/5 = 8).
I will make a slight digression so that Inverse Square Law is understood well. Without understanding this, talking about ISO will go over your head. I am a radar operator and I am forced to deal with Inverse Square Law. My radar can pick an aircraft up to 100 km by radiating energy of 100 kW power. If I want this aircraft to be picked up by my radar at 200 km, I have to feed the radar with 400 kW power. (Four times power to get twice the range). This is physics and we have to accept it. If I provide the radar with double the power (i.e., 200 kW), the aircraft will be picked up until 140 km only (1.4 times the distance with doubling the power).
With ISOs too, its just like boosting the power of a radar. At ISO 100 our GN is 40 metres, at ISO 200 our GN will be (40 x 1.4 = 56 metres), at ISO 400 the GN will be 80 metres, at ISO 800 the GN Will be (80 x 1.4 =112 metres) and so on and so forth.
We know about the aperture numbers. They progress like these f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32. It's interesting to note that every alternate number is doubling.
To understand more about Guide Number, Aperture values and other confusing terms in photography, you can check this blog of mine. http://photographypoints.blogspot.in/
Well both calculation here are somewhat correct but the right formula should be
$$\begin{align} \text{GN} &= \frac{\text{Aperture}\times \text{Distance}}{\text{ISO factor}} \\ \text{Distance} &= \frac{\text{GN}\times \text{ISO factor}}{\text{Aperture}} \\ \text{Aperture} &= \frac{\text{GN}\times \text{ISO factor}}{\text{Distance}} \end{align}$$
So if we're looking for the GN based on Aperture = f/8, Distance = 10 m, then our formula would be
$$\begin{align} \text{GN} &= \frac{8\times 10}{1} &= 80 \quad(\text{ISO 100})\\ \text{GN} &= \frac{8\times 10}{1.4} &= 57 \quad(\text{ISO 200})\\ \text{GN} &= \frac{8\times 10}{2} &= 40 \quad(\text{ISO 400})\\ \end{align}$$
*note the GN starts to lower if we change the ISO and maintain our Aperture and Distance setting
If we're looking for Distance based on GN = 40, Aperture = f/8 then
$$\begin{align} \text{Distance} &= \frac{40\times 1}{8} &&= 5\,\text{m} \quad(\text{ISO 100})\\ \text{Distance} &= \frac{40\times 1.4}{8} &&= 7\,\text{m} \quad(\text{ISO 200})\\ \text{Distance} &= \frac{40\times 2}{8} &&= 10\,\text{m} \quad(\text{ISO 400})\\ \end{align}$$
*note the Distance starts to increase if we change the ISO and maintain our GN and Aperture
If we're looking for Aperture based on GN = 40, Distance = 10 m then
$$\begin{align} \text{Aperture} &= \frac{40\times 1}{10} &&= f/45 \quad(\text{ISO 100})\\ \text{Aperture} &= \frac{40\times 1.4}{10} &&= f/5.6 \quad(\text{ISO 200})\\ \text{Aperture} &= \frac{40\times 2}{10} &&= f.8 \quad(\text{ISO 400})\\ \end{align}$$
*note the Aperture starts to narrow if we change the ISO and maintain our GN and Distance
