Flashgun Guide Number.

What is The Flashgun Guide Number?

To calculate the correct "ƒ" number for your camera to match the Flashgun three criteria need to be known.
(1) The guide number of the Flashgun in meters or feet, (usually found in the specifications documentfor the Flashgun or marked on the Flashgun itself).
(2) The distance to the subject from the flashgun in Meters or Feet.
(3) The ISO speed being used.

To calculate the "ƒ" number, divide the Guide Number by the Subject Distance.

For example:
A Flashgun with the guide number of 20 in Meters, (64 in feet), at ISO 100, with a subject at a distance of 2.5 Meters, (8 feet), would give an answer of ƒ8, (Guide Number 20 ÷ 2.5 Meters = ƒ8).
However at ISO 200, (a faster film speed) the calculation changes to, Guide Number 28 ÷ 2.5 Meters= ƒ11.

You could of course use this simple aperture calculator link button...

ISO Guide Number Formula:

The formula or calculation for a Guide Number is derived from a known ISO value and Guide Number and is attained like so...

Take the example given where the known ISO value is 100 and the Guide Number is 20, to get an answer of 20 from 100 the formula is...
The square root of 100 = 10.
The Guide Number 20 ÷ 10 = 2, so the key factor in this instance is "2" hence 2 x 10 = 20.

To find the Guide Number for ISO 200 the following applies...

√ 200 x 2 = 28.284, the nearest whole number to this is 28, so the Guide Number for ISO 200 is 28.

The reason we have to use a formula in this way is because we are dealing with aperture sizes and it is a common mistake to think that doubling the ƒ number halves the amount of light when in fact it is a factor of one quarter.
Because the aperture area is usually round, (not perfectly round because the aperture is made up from a number of overlapping elements enabling the hole to change size) the ƒ number is calculated as the area of a circle and to double circle area the following formula applies...

Example: To double the aperture size from ƒ16 to ƒ11 the formula is √16² ÷ 2 = 11.314, the nearest whole number to this is 11 so double the aperture size is ƒ11.

Light Path Distance:

It should also noted that the distance used in the formula is the distance the light has to travel from the Flashgun to the subject, not the distance the camera is away from the subject.
If "Bounce" flash is used, (for example refracting off of the ceiling) the distance to the subject is greatly increased due to the nature of the path the light has to travel.

Using the same set up example, if the Flashgun head was tilted to 45 degrees the distance the light travels to the subject would increase to 3.54 Meters even though the camera is still only 2.5 Meters away.
The calculation for the aperture setting now becomes, Guide Number 20 ÷ 3.54 Meters = 5.65 at ISO 100.
The nearest available ƒ number is ƒ5.6 which is now a bigger aperture than the previously used ƒ8 in fact it is double the area.