Guide No. & the Flash Formula

Guide Numbers and the Flash Formula

The GN (Guide Number) of a flash unit is a measure of the light energy that it produces in relation to the film or sensor sensitivity being used, and to what degree that energy is concentrated on the subject. Traditionally it was expressed for a beam angle corresponding to a standard camera lens - ie a 50mm lens in the case of a full frame camera, and the value of the GN for ISO 100 film was taken as the datum.

The use of the GN, put simply, is as a numerical value to be put in the Flash Formula, along with the subject distance, to obtain the recommended aperture for the camera lens.

While automation may hide it, the Flash Formula is always at work in flash photography. It is an expression of a law of physics and does not get out of date.

Let us start by stating the Flash Formula as it is usually seen, in Fig 1 :

Because F is a ratio (and thus technically dimensionless), but d is a distance usually expressed in metres or feet, GN is also expressed in metres or feet accordingly. I use metres in this article.

You probably already know or have heard of this formula, but stay with me, it gets more interesting, or you could say deeper.

Notice that neither the film/sensor ISO value nor the "focal length" of the flash unit's optics come into this version of the formula. In fact they should, because in this simple version of the formula the GN is a variable number which is not a good thing when we are talking about the same flash unit. But because photographers in the film days could not change film speed mid-roll (and probably used the same film most of the time), and flash units in the past usually had optics that were fixed with a beam angle to suit a standard lens, these factors were left out of the above simple version of the Flash Formula because they tended to be constant.

While you can evaluate the Flash Formula yourself, most flashguns with a manual capability (ie not entirely automated or built in to the camera) have either an engraved table of settings or some kind of slide rule on the body to do it for you. The slide rule might be linear or circular, and in most cases has no connection to anything in the interior. Later units can have an integral calculator and LED display. These aids do not usually mention the Guide Number value because it is implicit in their design.

Unfortunately, the tables or slide rules on film era flashguns do not go up to the high ISO values that digital cameras are capable of, typically no higher than ISO 800 or 1600, but it is possible to extrapolate from them mentally. The ISO number also might be displayed as an ASA number, but ASA is just an older name for the same thing. It might also offer a DIN number which is an even older standard; DIN 21 is the same as ASA 100 and ISO 100.

The Guide Number of a flashgun, as used in Fig 1 above, will vary with the film (or digital sensor) ISO value. ISO 200 for example is twice the sensitivity of ISO 100, so the lens aperture would need to be one stop less for the higher value. However, a reduction of lens aperture by one stop is increasing its F number by a factor of 2 (which is roundly 1.4) for example from F4 to F5.6. Therefore the ISO value must be taken into the flash formula as the square root of the ratio of the actual ISO sensitivity to a datum sensitivity, for which we can adopt ISO 100.

If we are given a datum Guide Number at a datum sensitivity, which we call GN(S0) and S0 respectively, the new Guide Number GN at a different sensitivity S will be given by Fig 4, and if we bring this into the simple flash formula of Fig 1 we get the more general form shown in Fig 5 :

For example if we are told the Guide Number of a flashgun is 20 metres at ISO 100, and we wish to use it with a digital camera set at a sensitivity of ISO 6400, according to Fig 4 the new effective Guide Number will be 160 metres. This is because 6400 is 64 times the datum ISO of 100 and the square root of 64 (ie 64) is 8, and 20 metres times 8 is 160 metres. We can now put this into the basic Flash Formula of Fig 1 and, for example, at a subject distance of 10 metres a lens aperture of F16 is recommended. Alternatively we can put the figures straight into the formula as expressed in Fig 5 and get the same answer.

Effect of Wide-Angle and Telephoto Flash Heads

Until around the year 1990, most flash units were sold with fixed optics that gave a beam angle suited to a lens with a moderately wide angle of view, typically a 35mm focal length on a 35mm or a 75mm focal length lens on a 6x7 camera etc. For wider angle lenses, adaptors were often available to clip to the front of the flashgun window to spread the beam more. A wide angle adaptor was not a diffuser (although one would do the job - less efficiently) but a plastic moulded matrix of lenslets.

If the camera is used with a telephoto lens, a standard flashgun will still do the job but not so efficiently, because some of its light will fall outside the subject area. Therefore telephoto adaptors were also available to narrow the flash beam, typically to suit a lens of about 100mm focal length on a 35mm camera. Longer lenses than that can still be used with them of course.

The GN does not change with a change of lens focal length, only with a change of the flashgun optics.

Later flashguns have integral zoom heads that the user could slide back and forth, with markings corresponding to lens focal lengths (invariable those of a 35mm camera). Into the digital era, some zoom heads were motorised to match the camera lens automatically.

The optics of flash heads are primitive. Large amounts of light are spilled outside the picture area and the effective coverage is only the central part where the illumination is tolerably evenly distributed. When it comes to the flash unit zooming, the optics get even worse because the zooming is done by moving a silvered reflector behind and around the flash tube that would ideally need to change its shape as it does so. If the optics were perfect, or anywhere near as good as the standards of camera lenses, the GN would increase linearly in relation to the nominal zoom length - a flashgun with a GN of 30 meters at a "standard" lens setting of 50mm, for example, would double to a GN of 60 metres when zoomed to its 100mm position.

In reality the GN at the telephoto positions fall significantly below the linear relationship. Two examples of actual flashguns with variable zoom heads are given in the tables below. When the Nikon SB-800 is zoomed from 50mm to 105mm, the GN rises from 44 metres to only 56 metres instead of the 92 metres that it would reach with ideal optics. In the case of the Vivitar 285HV, it rises from 36 metres to only 56, while 75 would have been ideal. Flashguns with zoomable heads typically have a 100-120mm maximum setting at which the GN is only about 30-50% higher than at 50mm, the setting for a standard lens.

Nikon SB-800

Focal Length
24mm 28mm 35mm 50mm 70mm 85mm 105mm
GN 30 32 38 44 50 53 56

Vivitar 285HV

Focal Length
24mm 28mm 35mm 50mm 70mm 85mm 105mm
GN n/a 21 31 36 n/a n/a 56

On the other hand, the two examples are doing better than the linear ideal at wide angle settings, such as at 28mm. This seems to be because flashguns spill a lot of light outside the subject area anyway, and the wide angle settings are bringing some of this back into use.

One could fit a mathematical curve to the relationship between a flashgun's zoom setting and its GN. It will be different for every flashgun. If we adopt a datum zoom setting, 50mm say, we can normalise the curve to be unity at the datum setting. If the flashgun's nominal zoom setting is Z, the value of the curve will be a function of Z, say fn(Z), which must be introduced into the Flash Formula as a modifier. This leads to a more general form of the Flash Formula shown in Fig 7 :

The point of this diversion is not for the user to evaluate this general form of the Flash Formula. The user would not know the shape of the curve fn(Z) without experimenting with a flash meter anyway. The point is to give a general understanding of the physics. I would hope however that the manufacturer does know the shape of the curve and informs the user in a table such as those of Nikon and Vivitar above, which are derived from their user manuals, and a modern digital unit offering a manual mode should have it in its software.

Until about the year 2000 is was customary for flashgun makers to give the GN of their units appropriate for ISO 100 and with a beam angle for a standard lens. It was often part of the name of the unit, for example the Pentax AT280T unit had a GN of 28 metres and the Sunpak G4500 hammerhead had a GN of 45 metres by this method.

Unfortunately, since then the marketing people have been stating Guide Numbers with the units at maximum zoom. This makes modern units sound more powerful than older units. However the GN at maximum zoom is probably of less practical interest than that at the standard lens angle, except to paparazzi, theatre photographers and sports photographers, and while portraits might be taken with a 100mm lens, direct flash from the camera position is hardly the best lighting for it. A more common situation for flash is a group or other informal indoor shot, for which a standard or wide angle lens is more appropriate.

Some manuals for modern units do not even state the GN for a standard or wide angle lens beam angle. The usual attitude is that the GN is just a marketing figure and in practice you should let the automation deal with it, but that is not helpful when trying to comparing the capability of different units when choosing one to buy.