If you had a flash with a guide number of 41 meters, and added another flash of the same type, how much greater would your total guide number be? (Hint: it wouldn't be double.) The answer is easy if you think in terms of stops.
When I started learning photography, the sequence of apertures seemed strange to me (1.0, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, etc.). I wondered why smaller numbers were used to represent larger apertures, and why they didn't use integers instead. After having relied on aperture priority most of the time for a while and having learned more about lighting, the f-number sequence is making more sense.
The f-numbers are ratios of the focal length to the diameter of the opening. See http://en.wikipedia.org/wiki/F-number The sequence of f-numbers conveniently follows the inverse square law, and remembering them can help you calculate some photography math problems quickly.
Here is the general procedure:
1. Analyze the question in terms of stops.
2. For each stop, find the corresponding number on the f-number scale, with 1 stop being f/1.4, 2 stops being f/2.0 etc. Here is the f-number scale in 1/3 stop increments:
1.0, 1.1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.5, 2.8, 3.2, 3.5, 4, 4.5, 5.0, 5.6, 6.3, 7.1, 8, 9, 10, 11, 13, 14, 16, 18, 20, 22
3. The f-number is your multiplier (if adding light) or divisor (if reducing light).
The procedure can be reversed as well.
EXAMPLE 1: ADDING FLASHES
In the foregoing example, if you wanted to know the combined guide number of two flashes (each with a GN of 41 meters), first think of the increase or decrease in stops. Because you're doubling the flash power, that would be equivalent to a 1 stop increase. Using the f-number scale, 1 stop up from f/1.0 is f/1.4. So the multiplier is 1.4. To increase the guide number of 41 meters by 1 stop, multiply by 1.4 to get 57 meters. Here's confirmation from someone with a light meter: see http://www.flickr.com/groups/strobist/discuss/72157605926174798/
Suppose you used 4 flashes? That would be 4x the light of the single flash, i.e., 2 stops. The corresponding f-number is f/2. The multiplier would therefore be 2.0, or a total guide number of 82 meters.
What if you wanted to use the Lastolite Tri-Flash bracket with 3 flashes? That would be triple the power of just one flash. Finding the total guide number would seem tricky at first but if you again think in terms of stops, it would be simplified. Triple the power would be 1.5 stops. Using the f-number scale, the f-number for 1.5 stops from f/1.0 is f/1.7. Using 1.7 as a multiplier, the total guide number of 3 flashes with a GN of 41 meters each would be a GN of about 70 meters.
EXAMPLE 2: COMPARING FLASHES
The SB-600 has a guide number of 30 meters at ISO 100 (at 35 mm zoom). Assuming that's true, if we used ISO 200, what would the equivalent guide number be? ISO 200 is 1 stop more than ISO 100, and the equivalent f-number on the f-number scale for 1 stop is f/1.4. The multiplying factor would therefore be 1.4, which means the guide number is 42 meters. And if we check out Nikon's website -- they indeed say the guide number is 42 meters at ISO 200.
What if we wanted to compare the power of an SB-800 to an SB-600? According to Nikon's website, the SB-800 has a guide number of 38 meters at ISO 100, at 35mm zoom. The SB-600 has a guide number of 30 at ISO 100, at 35mm zoom. (Manufacturers often inflate their guide numbers, but I'm supposing Nikon inflated the numbers for the SB-800 and SB-600 consistently.) The ratio of 38 to 30 is 1.26, which is a bit more than 1.2 (which would be 2/3 stop), which means the SB-800 has a bit more than 2/3 stop advantage over the SB-600.
Are you wondering how much more powerful is an AlienBee strobe compared to an SB-800? The SB-800 has a claimed guide number of 184 feet when zoomed to 105mm (ISO 100). With an 11-inch reflector, the B400 has a guide number of 220 feet (ISO 100). With an 11-inch reflector, the B1600 has a guide number of 450 feet (ISO 100).
Comparing the B400 to the SB-800: the ratio of 220 feet to 184 feet is 1.19 or around 1/2 stop to 2/3 stop.
Comparing the B1600 to the SB-800, the ratio of 450 feet to 184 feet is 2.44 or about 2.5 stops.
Comparing the B1600 to the B400, the ratio of 450 feet to 220 feet is 2.05, i.e., 2 stops.
EXAMPLE 3: INVERSE SQUARE LAW
Let's say you want a black background for your subject (let's define black for our purposes as 3 stops underexposure). Suppose the subject is properly exposed while at 10 feet away from the flash. How far away should the background be (assuming both the subject and background are gray) to become 3 stops underexposed (relative to the subject) from the same flash? Cross-referencing 3 stops with the f-number scale, we see the corresponding number is 2.8. That means the background has to be 2.8x further from the flash than is the subject, i.e., 28 feet away.
Right-Brained Guide to Combining Guide Number of Multiple Flashes