Flash intensity falls off with distance. Guide Number is a numerical method used to determine exposure of direct flash for manual flash power levels, to automatically deal with the Inverse Square Law, making the math be trivial. The reference base is a known accurate Guide Number for one situation, from which other situations can be calculated. There are also other ways, today we might use a handheld flash meter, or metered TTL, or just trial and error works well with the digital LCD preview. But in the old days (including flash bulbs), guide number was all we had. The concept is still valid and useful, and is still a fundamental for understanding flash. Guide Number is a solution to deal with the Inverse Square Law.
The full details explaining use of guide numbers are below the Guide Number Calculator.
Please report ( Here ) any problems with the calculator, or with any aspect of this or any page. It will be appreciated, thank you.
Insufficient flash exposure is corrected with wider aperture, shorter distance, higher ISO, or more flash power.
Excessive flash exposure is corrected with stopped down aperture, longer distance, lower ISO, or less flash power.
There are three ways to use this GN calculator.
Repeating again: NOTE that if your flash specifies Guide Number for 105 mm zoom, but you are using it at 24 mm zoom, you absolutely need to know and use the 24 mm zoom Guide Number (see your flash manual for a standard Guide Number chart).
Guide Number (GN) is a primary fundamental, related to Inverse Square Law, and is about how light works, which will always be important to know. The light fall off means that direct flash exposure can be correct at only one specific distance from the flash. Anything closer is brighter, and anything farther is darker. But how much it changes works on sort of an exaggerated percentage basis (inverse square law), and a greater distance simply has more middle ground range. Bounce flash can seem to extend this range, but direct flash exposure falls off with the square of the distance. Flash will be two stops underexposed at twice the distance, or two stops overexposed at half the distance (inverse square law). So the general rule for flash is to keep all of your subject parts near the same distance plane from the lights (same idea as focus depth of field).
Photographing groups: The same distance plane is impossible for multiple rows, and multiple rows can be a deep zone for an even flash illumination, or for focus depth of field too. For long rows, curving the ends forward to equalize the distance helps. For large groups of a few rows deep, raising camera and flash height dramatically (with step ladder) to look down into the group can minimize difference of row distances (and won't hide faces with rows in front). Greater flash distance can extend the range of acceptable flash exposure. We normally think umbrellas ought to be "close as possible" for softness, but when back twenty feet, umbrellas don't add much benefit (will cost power, and softness is not important then anyway). However, increasing the flash distance for greater flash exposure range, and stopping the lens down for greater depth of field, very significantly increases the flash power needed. Common notions for best group lighting for multiple rows is that multiple flashes ought to all be above the camera, pointing outward to cover the group evenly (lights at the camera see same as what the lens sees, without creating terrible shadows). Two flashes aimed different directions are individual units, NOT combining the same as multiple flashes ganged acting as one. But be careful about any central overlap, which is ganged. It would be good to meter the lights and the center, to verify all group areas are equal. For large groups, see Google  I'd suggest the Chuck Gardner link there.
This diversion is really about the distance range depth extents of the flash exposure. If you meter the flash, you can meter at the range extents too (you certainly ought to plan and know the exposure difference at front and rear of a big group). Or if direct flash, use the calculator here. Or if computing guide number, simply computing distance at ± 1/3 stop apertures computes the range extents for that tolerance (Note ± 1/3 stop is 2/3 stop from front to rear). Exposure range is not exactly about power or aperture, but is about the flash distance (inverse square law), so as to distance, the range distance is applicable to TTL too.
Guide number makes exposure computation very easy. Guide number is the oldest system to determine flash exposure (used for flash bulbs, before automation), but guide number only applies to direct flash. Guide number is not useful for bounce, because it requires knowing the distance in the total path from flash to subject, and also the reflection coefficient at the ceiling (very roughly, common situation bounce can need 2 or 3 stops more power than direct flash). But guide number still is fundamental today, and understanding guide numbers can increase understanding of flash and inverse square law, whether you actually use guide numbers or not. We should all spend a little time playing with this, to understand the concept. It is a genuine basic of flash photography, which simplifies the Inverse Square Law (which is a really huge factor for flash).
Shutter speed is not a factor of flash exposure (Part 2), but f/stop, ISO, flash power, and flash distance are the factors. Distance does not affect our sunlight, but it is pretty tricky for flash. Direct flash exposure falls off with the Inverse Square Law (with distance), a serious complication for determining exposure. If we don't actually meter the flash, then guide numbers can solve distance computation easily (for direct flash). Guide numbers have been calculated forever, at least since first commercial flash bulb about 1930. Guide number was the only system before light meters and electronic automation.
If you meter your flash, either via TTL flash automation, or by using a hand held flash meter, or if you just use the camera's rear LCD and histogram to tweak in your manual flash exposure, then maybe you can get by for awhile without it, but Guide Number certainly does help basic understanding, essential fundamentals of flash that we should know (how direct flash falls off with distance).
So that's good to know to know, but guide number tells a lot more. If we know guide number is GN 40 (feet), then we know that 8 feet will need to use GN 40 / 8 feet = f/5 exposure. That is a lot to know (again, this is for unmodified direct flash).
Guide Number is a tool to determine exposure of direct flash with manual flash power levels, to automatically deal with the Inverse Square Law, making the math be trivial.
Guide Number = f/stop x Distance (those values which actually give a proper exposure)
f/stop = Guide Number / Distance (aperture for other distances)
Distance = Guide Number / f/stop (distances for other apertures)
For any given "correct flash exposure" situation, guide number is simply numerically equal to the aperture number (like the number 8 in f/8) multiplied by the subject distance (like 10 feet). Then for example, the guide number is f/8 x 10 feet = GN 80 (feet units). Specifically, that aperture and distance combination which gives the correct exposure, defines the guide number.
The Distance is from flash to subject. The flash might be on the camera, but the camera position is Not a factor. It is about the flash.
The useful part is that this guide number is a constant for that flash situation, good also for other distances or other apertures. If we know GN for the situation (flash power level and ISO), we can know correct direct flash exposure for any distance or any aperture. This constant GN is initially determined by some trial situation seen to give correct exposure. Or we can use the manufacturers chart of guide number (trial is what they did).
If for example, in any situation at all, if f/8 is seen to give the correct exposure at 10 feet (from the flash), then this defines that the guide number for this situation is determined to be 80 (feet, from f8x10 feet). Whatever situation gives a correct exposure, that determines the actual guide number, by definition.
The overwhelming advantage of knowing this guide number constant is that if we then move the light to be 5 feet from subject, then GN 80 tells us that GN 80 / 5 feet = f/16 will give us correct exposure there too. Or if we open the aperture to f/4, then the correct distance for this flash power will be GN 80 / f4 = 20 feet. This guide number 80 is a constant (in this same flash power situation), for any distance and any aperture, and its purpose is to make the inverse square law be trivial to compute.
Said again From knowing this guide number constant (GN = aperture x distance) for one flash situation (power and spread angle), we can recompute any other aperture/distance combination for correct exposure, which automatically takes the inverse square law into account, involving only the simplest division. For example, if we know the guide number is 80 (feet), then we immediately know that all of these combinations give the same correct flash exposure:
If we know the correct exposure, then we know GN:
f/8 at 10 feet = GN 80

Or, if we know the guide number is 80, then we know exposure:
GN 80 / 10 feet = f/8

You get the idea  any combination computing (f/number x distance) = GN 80 (in this example) also gives the same correct manual flash exposure. The main use is, if our subject is at 14 feet (from the flash), then we know GN 80 / 14 feet = f/5.7. This is a lot to know by simple division, and it really could not be any easier.
This works (and is conveniently used) because Guide Number definition is (distance x f/stop), therefore doubling GN doubles distance range (4x the light), OR doubles actual f/stop Number (1/4 the light), which is two stops either way. Actually for any number N, any GN gives same exposure at (N x distance) if using (fstop number / N). The N cancels for GN. This is true because of the coincidence that distance observes the inverse square law, and the area of f/stop number observes the square of the radius.
Where do we get this guide number? Whatever aperture and distance that gives an actually correct exposure can compute guide number. Or more commonly, there is also a guide number specification in the flash manuals (see next page). Then we only need to know the distance between flash and subject. This guide number is speaking of manual Direct flash, and this guide number will change if you zoom the flash head differently.
Zoom: Zooming the flash head changes the guide number. Zooming in, to match the lens zoom (a more narrow coverage angle), also concentrates the flash power into a more narrow brighter beam appropriate for the lens zoom, with a higher guide number. There will be a guide number chart in the flash manual, with a different guide number for very zoom value. See the sample guide number chart next page.
Flashes that do not zoom (like the DSLR camera's internal flash) will have one guide number value. It is printed perhaps as (the Nikon D3200 specification chart):
"Guide Number: Approx. 12/39, 13/43 with manual flash (m/ft, ISO 100, 20 °C/68 °F)"
For manual flash, this says GN 13 (meters) / GN 43 (feet). This implies at full manual power, but we can turn the flash power down as necessary, which lowers the guide number.
You can work in units of either feet or meters. Since there are 3.28 feet in one meter, the GN in feet is simply 3.28 times the GN in meters. Again, see the guide number chart in the flash manual for flashes that zoom (an example chart is next page).
Guide number is all we had in the old flash bulb days (and it still works), and before flash units zoomed, they always had a little calculator on them to do this guide number division, but TTL flash mode has made guide numbers less used today. The top few Nikon flashes have a GN Mode, which is a GN calculator (sets flash power level to the aperture and distance). But we can often do the rough math in our heads (if distance is about 10 feet, then GN / 10 = aperture), which often gives a close starting point for proper flash exposure.
The published guide numbers (specs, charts, etc) are for unmodified direct flash and for the specified flash head zoom level. As the speedlight zooms in (longer mm to follow the lens zoom), the reflector concentrates the flash power into a smaller angle that becomes brighter, to cover the same appropriate view that the zoomed lens sees. There will be a different guide number for every zoom setting, and for every power level. Any other reflector situation  lighting modifier (diffusion dome, reflector, bounce, umbrella, whatever)  is a very different guide number. Any other path than direct flash is a different subject (involving longer path and bounce reflection losses, etc).
Guide number makes Inverse Square Law math be easy. The reason this product (of Distance x f/stop) works as a constant for exposure is due to the coincidence that each stop of f/stop numbers increase by the square root of two (1.414) to give half intensity, and the Inverse Square Law distance decreases by the square root of two to give double intensity, and these square factors of 2 offset and cancel in the math, so that the simple product (aperture x distance) is a CONSTANT for correct exposure for this given direct flash situation (ISO, zoom, power level), for any aperture or any distance. It is enough to know that the big deal is that the Guide Number automatically accounts for the Inverse Square Law, making its math be almost trivial for us. This is a big deal, but it is only applicable to bare direct flash.
Or even easier... Flashes compatible with the camera (communication) often know f/stop, ISO and zoom from the hot shoe. So in direct flash Manual mode, they can use their guide number to show the distance calculation (appropriate for the current power level) on their LCD. This can be a fine starting point (again, direct flash only). Can be very helpful.
ISO: The guide number conversion charts in the flash manuals are typically printed showing ISO 100 values, and then we know that GN increases by square root of 2, or by 1.414x for every doubled step of ISO. Or we divide GN by 1.414 if converting to half of ISO.
ISO  25  50  100  200  400  800  1600  3200  6400 
GN  x0.5  x0.707  x1  x1.41  x2  x2.83  x4  x5.66  x8 
This first chart is a normal GN conversion chart, always aligning ISO 100 with GN 1x multiplier, because ISO 100 is usually of interest to us. Aligned that way, you have that standard chart just above.
But the rows are individually scrollable. This is something easy, but possibly made confusing here.There are no absolute relationships, we can slide these scales left or right as appropriate to our lighting situation. The meaning of the default values initially shown in this chart should be that IF you are using ISO 400, and align GN x1 there too (if ISO 400 is your base GN x1 value), then all other ISO values still have the GN multipliers shown. The doubling effect just mentioned always exists. For example (as shown initially), IF using ISO 400 and assuming it is the base at GN x1, then the next multiplier to the right gives the GN multiplier for the next ISO to the right (ISO 800 is 1.41x GN of current GN for ISO 400). And IF that combination also aligns an actual flash power level (like 1/4 power), then the GN multipliers also work for other power levels. Or, the GN calculator above will do all of this too.
The guide number is multiplied or divided by 1.414x for each stop changed, which is each doubling of ISO, or for each doubling of flash power level. Two sequential doubles of ISO or power level doubles GN.
Then since GN = f/stop x distance, then we know doubling GN also doubles the computed f/stop number (which is two stops), or it doubles distance range (which is two stops).
The flash power level steps of Full, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 are each half power of the previous step. The best fact to know about manual flash is that each half power step is one f/stop of exposure. One stop is a 2x factor, so said again, turning the flash from 1/4 to 1/8 power (which is half) reduces the exposure by one f/stop. This is extremely convenient to know.
Each half power step reduces GN by the square root of 2 (divide GN by 1.414). Two half power steps (1/4 power) is two stops of exposure, or 1/2 the GN value. Or use the calculator, or see the GN chart on next page.
If the speedlight does not zoom, then that's all it can do, so you can only compare that. But if it zooms, increasing the flash zoom mm number concentrates the power into a smaller beam. Doubling the zoom mm theoretically covers a 1/4 smaller area with 4x brighter intensity, two stops. Which theoretically, the calculator could calculate the areas, but the actual reflectors vary to much to try. There is substantial area overlap (so frame edges are fully exposed), and usually double zoom mm might multiply guide number about 1.4x, or one stop (if that). Which is only a very rough approximation  because again, of course it depends on the individual reflector design. But guide number maybe about doubles from 24 mm to 105 mm (4x), which is near a two stop increase (half expected), but there are large variations. I'd love to be able to add zoom to the GN calculator, it is obviously an important factor, but this would have to embed GN charts from many different specific flashes, and there are too many flashes. You can do that easier, so instead see the Guide Number chart in your flash manual.
Use either feet or meters with the calculators, but be consistent with GN and Distance.
If the flash can zoom, then it is required to compare Only at the Same zoom values. Because zooming in concentrates the same flash power into a smaller area, which is then brighter (but is only useful in that smaller area). If comparing GN of a speedlight to a studio flash, then to have any meaning, only the same reflector angular coverage (that was used for the GN rating) must be compared (softboxes and umbrellas drastically change GN and coverage). If it does not zoom, then of course it only has that one setting to do one thing (with that same reflector). It used to be that speedlights that zoom agreed to advertise guide numbers at the same standard 35 mm zoom, which was considered to be a typical useful working value, certainly conceivable (it was about full frame views then, and the major Japanese flashes still do this). The power was comparable that way, at the same 35 mm zoom. But today, FX and DX sensor coverage can change GN at the same zoom. So, just saying, for power comparisons to be meaningful, all things must be equal.
But today, some marketing (especially Chinese flashes) advertise their maximum 105 mm zoom guide number, simply because that is a larger number that looks better than others, regardless that we rarely use flash at 105 mm zoom.
Today, to know very much about ratings, we need to look at the guide number chart in the user manual (sometimes online). Comparing this calculation can be useful when shopping for a flash. However, I have seen one Chinese manual that simply advantageously had the wrong chart in it.
If one GN is rated for ISO 200, then dividing that number by 1.414 will give the ISO 100 equivalent. Guide Number can only be compared if both are at the same flash zoom and ISO settings.
Guide Number is used for speedlights, but is not very meaningful for studio flash. One reason is they are typically not used as direct bare flash, but also their GN rating situation is so unknown.They don't zoom, but comparison is difficult when we may not know what reflector was rated, or what its angular distribution spread is. Speedlight GN varies over probably a 2 to 1 range when they zoom... but we can only compare intensity when lighting the same angular coverage, when doing the same job.
Studio lights, saying it again: Guide Number works very well for unmodified direct flash. One big issue is that guide number cannot be specified for bounce or umbrellas, etc. (because, it depends on them). So typically, direct bare flash is much less important for studio lights, because we normally heavily modify their light with umbrellas, softboxes, grids or snoots, whatever. This drastically changes their distribution coverage angles, and every different reflector coverage would create very different guide numbers. The guide number that is specified for a studio flash may apply to the included standard reflector it ships with, but if the applicable reflector used to specify GN is not specified, then we have no clue what its GN means for our usage. Any wider reflector providing wider area coverage will have a lower guide number, and a more narrow reflector concentrating the light into a smaller area will have a higher guide number. To be able to compare guide numbers, we need to compare at the same area coverage. So guide numbers are typically more common of camera hot shoe speedlights (direct flash), and speedlights do provide specifications for Guide Number at each zoom as a guide to the flash power and its distance capability (again, it only applies to bare direct flash). For studio lights, GN has less and unknown meaning, and probably does not apply to your usage, since these normally use various modifiers (umbrellas, softboxes, etc). So studio lights are likely metered.
Resulting GN of ganged multiple flashes
This context of ganged means flashes probably all mounted on the same stand, and aimed at the same point, specifically acting as one. A Main light and Fill light situation is acting as two, and is NOT two ganged acting as one.
The GN of multiple equal flashes ganged in combination acting as one, is GN of one times square root of (number of flashes). Each doubling of the number of equal flashes (from 1 to 2, or 4, or 8 flashes) results in one stop in brightness, each doubling increases GN by the square root of 2 (1.414). Two or four flashes may be reasonable, but thereafter, the law of diminishing returns will apply.
But ganging two unequal flashes acting as one, say of GN 58 and GN 80 (0.93 stop difference), will add as square root of (58² + 80²) = GN 99. This total is +1.54 EV compared to this smallest flash (more than double), and +0.61 EV compared to this largest flash (less than double).
Continued  More Guide Numbers next page (charts, etc).