The guide number for an electronic flash measures its ability to illuminate the subject to be photographed at a specific film or sensor sensitivity and angle of view. A higher guide number indicates a more powerful flash.
For example, doubling the guide number means the flash can illuminate an object at twice the distance, or for an object at the same distance can be used at one quarter the sensitivity. Doubling the guide number requires a quadrupling of the flash's power, as the area to be illuminated increases as the square of the distance (cf. inverse-square law).
This simple relationship is well-defined because the brightness of a flash falls off with the square of the distance, but the amount of light admitted through an aperture decreases with the square of the f-number.
The guide number represents an exposure constant for a flash unit. For example, a guide number of 80 feet at ISO 100 means that a target 20 feet away will be correctly illuminated with an aperture of f/4 (80 = 20 × 4) using a sensitivity of ISO 100. For the same guide number and an aperture of f/8, the light source should be 10 feet from the subject (80 = 10 × 8).
Guide numbers do not depend on the focal length of the lens: the distance a flash can illuminate does not depend on the angle of view of the lens. However, some flashes have the capability to "zoom with the camera" and concentrate their light into a narrow beam for use with a telephoto lens. Since the light from the flash is more concentrated, this increases the guide number. Manufacturers typically advertise the guide number for their flashes at the narrowest setting. For instance, the Olympus FL-50 has a guide number of 50m at ISO 100 when set to its narrowest setting, but significantly less when illuminating a wider area.
Guide numbers can be given in feet or metres, and are usually given for ISO 100 sensitivity. The guide number of 80 feet in the previous example corresponds to a guide number of approximately 24 metres. The calculations remain the same: a target 6 metres (20 feet) away requires an aperture of f/4 (24 = 6 × 4). Thus, when comparing flash units, make sure to compare the guide numbers, measured in the same unit, for the same ISO rating and the same focal length "zoom" setting of the flash.
The distance in the guide number calculation is the distance from the flash to the subject. The position of the camera is not relevant.
All the above would be absolutely true if we were dealing with a simple open light source, such as an old-fashioned incandescent bulb or a candle. However most small hotshoe-mounted flashguns (strobes) emit a focused beam of light that doesn't obey the inverse square law in the simple way previously described. It can be easily and practically verified that a focused beam does not follow the simple inverse square law by measuring the light intensity of a household torch or theatre spotlight beam at various distances from the lamp.
With a focused beam, the apparent or virtual origin of the light is behind the source itself, and it's this virtual origin from which the distance must be measured in order to calculate the f-number from the guide number. Unfortunately this information is not given by any manufacturer, nor is it easily measured by the user, and in any case the distance from the real light source to its virtual origin varies with the zoom setting of zoom-headed flashguns. This leaves guide number calculation as a very rough guide to exposure at best, and in some practical situations it can give grossly inaccurate results.
The flash-to-subject distance is longer when bounced flash is used, and the illumination is less when a diffuser is attached to the flash unit. In the former case it is possible to calculate the flash to subject distance that the light travels along the bounce path instead, but this still does not take into account the loss of light due to incomplete reflection. Most photographers apply a rule of thumb such as opening up by one to two stops. However, nearly all flashes available now have an automatic exposure capability that will automatically provide the correct illumination regardless of diffuser or bounce use; the guide number is mostly useful for comparing the maximum light output of several flash units.
Guide numbers are especially useful in dealing with manual flash units when calculating the aperture for a particular exposure or the maximum flash range for a given aperture. In practice, it's normal to know the guide number and the distance and need the aperture, so the equation is rearranged to give:
f-number = GN/distance
Some flash units have a dial on the back (in fact, a simple form of slide rule) or a chart to help in calculating the desired settings.
The aperture given by the guide number is only correct for certain locations, generally indoors where a reasonable amount of "stray" flash light will be reflected from surrounding walls onto the subject. The effective GN is slightly lower outdoors as any light not falling directly on the subject from the flash will be lost.