# 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.

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.

• Thank you! Now it all makes sense! I guess the author of the formula meant ISO-factor not just ISO which is equal 1 for ISO = 100; 1.4 for ISO = 200; 2 for ISO = 400 etc. Duh! Oct 31, 2011 at 19:40
• Yeah, I was just updating my answer to say that. :) Oct 31, 2011 at 19:41
• I’m glad I found above info. I have a question here. By the way, shall I know if above formula is based on 1/1 full power with bare strobe or with like softbox? Jul 5, 2018 at 14:00

The formula you found with ISO included is wrong.

The correct formula is....

Guide Number= Distance x Aperture. or Distance = Guide Number / Aperture or Aperture = Guide Number / Distance

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 mtrs, 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 iam forced to deal with Inverse Square Law. My radar can pick an aircraft upto 100kms by radiating energy of 100KW power. If i want this aircraft to be picked up by my radar at 200kms, i have to feed the radar with 400kw 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 200kw, the aircraft will be picked up till 140 kms 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. Its 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

GN = (Aperture*Distance)/ISO factor
Distance = GN/(Aperture/ISO factor)
Aperture = GN/(Distance/ISO factor)

So if we're looking for the GN based on Aperture=f8, Distance=10m then our formula would be

GN=(8*10)/1 ISO 100 =80
GN=(8*10)/1.4 ISO 200 =57
GN=(8*10)/2 ISO 400 = 40

*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=f8 then....

Distance=40/(8/1)= 5m ISO 100
Distance=40/(8/1.4)= 7m ISO 200
Distance=40/(8/2)= 10m ISO 400

*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=10m then....

Aperture=40/(10/1)=f4 ISO 100
Aperture=40/(10/1.4)=f5.6 ISO 200
Aperture=40/(10/2)=f8 ISO 400

*note the Aperture starts to narrow if we change the ISO and maintain our GN and Distance

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

the square root of (ISO/100).

In keeping with the use of a series of examples:

the square root of (200/100) is 1.4
the square root of (400/100) is 2
the square root of (800/100) is 2.8, etc.

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:

http://www.discoverypark.info/effective_guide_number.htm