View source for Guide number

{{Short description|Photoflash exposure setting measurement}}
[[File:Vivitar 285 guide numbers.jpg|thumb|right|300px|A scene will be properly illuminated for every combination of f{{nbhyph}}stop and distance shown on this flash device's exposure calculation dial, each of which equals the same '''guide number'''.

The guide number here (full power setting, ISO 100, and normal-angle coverage) is '''37''' for calculations made in meters (yellow arrow) and '''120''' for feet (orange). For instance, on the foot scale, {{f/|4}} × 30&nbsp;ft = 120, as do both {{f/|8}} × 15&nbsp;ft and {{f/|16}} × 7.5&nbsp;ft. In meters, {{f/|1.4}} × 26&nbsp;m = 37 as do {{f/|22}} × 1.7&nbsp;m and every combination between.]]

When setting [[Flash (photography)|photoflash]] [[Exposure (photography)|exposures]], the '''guide number''' ('''GN''') of photoflash devices (flashbulbs and electronic devices known as "studio strobes", "on-camera flashes", "electronic flashes", "flashes", and "speedlights")<ref group=note>The Nikon brand name for its camera-mounted electronic flash products, ''Speedlight'', is frequently used in lowercase form (''speedlight''<sup>&thinsp;</sup>) as a generic term for [[hot shoe]]-mounted electronic flash devices while Canon uses the trade name ''Speedlite''.</ref> is a measure photographers can use to calculate either the required [[f-number|f{{nbhyph}}stop]] for any given flash-to-subject distance, or the required distance for any given f{{nbhyph}}stop. To solve for either of these two variables, one merely divides a device's guide number by the other.

Though guide numbers are influenced by a variety of variables, their values are presented as the product of only two factors as follows:<ref>B & H Foto & Electronics: ''[https://www.bhphotovideo.com/explora/photography/tips-and-solutions/understanding-guide-numbers?BI=572&c3api=0980,144904813851&gclid=CPmXgJT4udUCFRSVfgodPPYH3g Understanding Guide Numbers]''</ref>

::Guide number = f-number × distance

This simple inverse relationship holds true because the brightness of a flash declines with the square of the distance, but the amount of light admitted through an aperture decreases with the square of the f-number.<ref name="Scantips">Scantips.com: ''[http://www.scantips.com/lights/flashbasics1c.html Understanding Flash Guide Numbers, plus GN Calculator]''</ref> Accordingly, as illustrated at right, a guide number can be factored to a ''small f{{nbhyph}}number times a long distance'' just as readily as a ''large f{{nbhyph}}number times a short distance''.

Guide numbers are not an absolute measure of flash power<!-- EDITORS: "POWER" IS UNIVERSALLY A TERM USED IN THE INDUSTRY TO REFER TO POWER SETTINGS AND LIGHT OUTPUT. WHEN USED THIS WAY, POWER IS BEING USED IN ACCORDANCE WITH ONE OF ITS DEFINITIONS ("the ability to do something or act in a particular way") AND IS PERFECTLY CONSISTENT WITH INDUSTRY PRACTICES. THIS USAGE IS DIFFERENT FROM THE SCIENTIFIC MEANING, WHERE IN THE SCIENCE OF LUMINOUS EXPOSURE, A MORE POWERFUL FLASH IS MORE "ENERGETIC". THE ARTICLE USES "POWER" TO DENOTE "ABILITY" WHEREVER NECESSARY TO EFFECTIVELY COMMUNICATE USING COMMON VERNACULAR AND USES "ENERGY" IN PASSAGES REQUIRING SCIENTIFIC RIGOR.) --> (a property called [[luminous energy]]) because they are influenced by other variables, notably the camera's ISO setting ([[film speed]]) and flash coverage angle.<ref group=note><!--

 -->Studio strobes in particular are often rated in [[watt second|watt⋅seconds]], which is an absolute measure of illuminating power but is not particularly useful for calculating exposure settings.</ref><!--

 --> For any given ISO setting and coverage angle however, an inherently more powerful flash device featuring a guide number that is, for instance, twice as great will permit subjects to be properly exposed from twice as far away for any given f{{nbhyph}}stop, or conversely, will permit scenes at a given distance to be properly exposed at an f{{nbhyph}}number twice as great.<!-- EDITORS NOTE: Two terms are used in this article regarding apertures: "f-number" and "f-stop". The term "f-number" is used in reference to A PARTICULAR VALUE of an aperture ratio. The term "f-stop" is used in reference to AN INCREMENTAL CHANGE in aperture ratio (e.g. "a difference of two f-stops". -->

The guide number system, which manufacturers adopted after consistent-performing mass-produced [[Flash (photography)#Flashbulbs|flashbulbs]] became available in the late 1930s, has become nearly superfluous due to the ubiquity of electronic photoflash devices featuring variable flash output and automatic exposure control, as well as [[digital camera]]s, which make it trivially easy, quick, and inexpensive to adjust exposures and try again.<ref>{{cite book|last1=Jacobson|first1=Ralph|title=Manual of Photography|date=2000|publisher=Focal Press|isbn=978-0-240-51574-8|edition=9th|page=[https://archive.org/details/digitalvideocame00pete/page/331 331]|url-access=registration|url=https://archive.org/details/digitalvideocame00pete/page/331}}</ref> Still, guide numbers in combination with flash devices set to manual exposure mode remain valuable in a variety of circumstances, such as when unusual or exacting results are required and when shooting non-average scenery.

Different models of flash devices available on the market have widely varying maximum-rated guide numbers.<ref group=note>For example, among [[hot shoe]]-mounted flash devices, at ISO 100, 60° horizontal coverage angle (suitable for use with a 35&nbsp;mm-format, full-frame lens with a 35&nbsp;mm focal length), and full power, the Holga ''Holgon MF Flash'' has a guide number of 6.5&nbsp;(m). Under the same conditions, both the Sony ''HVL-F58AM'' and the Metz ''mecablitz 64 AF-1 digital'' have guide numbers of 36&nbsp;(m). And still under the same conditions, the side-mounted pistol grip-style Metz ''mecablitz 76 MZ-5 digital'' is rated at 45.5&nbsp;(m).</ref> Since guide numbers are so familiar to photographers, they are near-universally used by manufacturers of on-camera flash devices to advertise their products' relative capability. However, such a practice demands industry-wide standardization of both the ISO setting and illumination angle underlying the ratings; this has only been partially realized. For the most part, manufacturers state guide numbers relative to a sensitivity of ISO 100.<!--

 --><ref name="List">One notable way of expressing guide numbers scaled for use with both feet and meters (and relative to an ISO setting of 100) is as practiced by Metz mecatech GmbH, as exemplified by the data sheet for their ''mecablitz 52 AF-1 digital'' ([https://www.metz-mecatech.de/en/lighting/flash-units/system-flash-units/mecablitz-52-af-1-digital/data-sheet.html product page here]):<!--

-->{{Quote frame|'''Flash output'''<br />• High max. guide number 52 (meters), High max. guide<br />number 170 (feet) for ISO 100/21° and 105 mm}}<!--

-->Another notable example is Nikon's practice for expressing the technical specifications of products marketed in the U.S., such as their ''SB-5000 AF Speedlight'' ([http://www.nikonusa.com/en/nikon-products/product/flashes/sb-5000-af-speedlight.html#tab-ProductDetail-ProductTabs-TechSpecs product page here]):<!--

-->{{Quote frame|'''Guide Number'''<br />34.5 m/113 ft. (at 35&nbsp;mm) 55<br />m/180 ft. (at 200&nbsp;mm) (FX<br />format, standard illumination<br />pattern) (at ISO 100)}}<!--

-->Yet another notable example is Canon USA's practices, as exemplified by their ''Speedlite 430EX III-RT'' ([https://www.usa.canon.com/internet/portal/us/home/products/details/cameras/flashes/speedlite-430ex-iii-rt product page here]), which is as follows:<!--

-->{{Quote frame|'''Guide Number'''&nbsp;&nbsp;The maximum Guide No. is approximately 141.1 ft./43m at ISO 100 and 105&nbsp;mm flash coverage.}}</ref><!-->EDITORS: PLEASE DO NOT EDIT THE TEXT SHOWING THE MANUFACTURERS' AD COPY. THOUGH A SPACE SHOULD SEPARATE THE NUMERIC VALUE OF A MEASURE AND THE UNIT OF MEASURE, LIKE "43 m", CANON DID NOT</!--> However, manufacturers sometimes rate guide numbers at ISO 200, which makes them 41% greater.<ref name="ISO200">Nikon, for instance, gives ''two'' ratings when providing the technical specifications for their ''SB-910 AF Speedlight'', one of which is relative to ISO 200 ([http://www.nikonusa.com/en/nikon-products/product-archive/flashes/sb-910-af-speedlight.html#tab-ProductDetail-ProductTabs-TechSpecs product page here]):<!--

-->{{Quote frame|'''Guide Number'''<br />34 m/111.5 ft. (at ISO 100,<br />35mm zoom head position, in<br />FX format, standard<br />illumination pattern,<br />20°C/68°F) to 48&nbsp;m/157.5 ft.<br />(at ISO 200, 35&nbsp;mm zoom<br />head position, in FX format,<br />standard illumination pattern,<br />20°C/68°F)}}</ref><!--

 --> Furthermore, the illumination angles underlying manufacturers' ratings vary greatly, which can make it particularly difficult to compare models.
{{TOC limit|3}}

== Understanding guide numbers ==
=== Units of measure ===
[[File:Distance times fstop.jpg|thumb|right|302px|Guide numbers are a composite unit of measure comprising two factors: ''aperture ratio'' and ''distance''. Guide numbers may be expressed in either of these units of measure: {{nowrap|''f{{nbhyph}}number⋅meters''}} or {{nowrap|''f{{nbhyph}}number⋅feet''.}}]]
Throughout most of the world where the metric system ([[International System of Units|SI]]) is observed, guide numbers are expressed as a unitless numeric value<!-- EDITORS: PLEASE DO NOT LINK TO OUR “DIMENSIONLESS QUANTITY” ARTICLE. FOR ONE THING, THAT ARTICLE IS INTERNALLY INCONSISTENT. SECONDLY, “DIMENSIONLESS QUANTITY” IS A MORE ABSTRUSE TERM THAT DRAWS ATTENTION TO ITSELF. THIRDLY, JUST BECAUSE ONE *CAN* LINK TO ANOTHER ARTICLE, ONE SHOULDN'T DO SO UNLESS THE LINK IS TRULY GERMANE TO THE SUBJECT MATTER (FLASH PHOTOGRAPHY). IN THIS CASE, IT'S FAR OFF-TOPIC. SEE “User:Greg L/Sewer cover in front of Greg L's house” END NOTE--> like '''34''', even though they are technically a composite [[units of measure|unit of measure]] that is a two-[[Multiplication|factor]] [[product (mathematics)|product]]: {{nowrap|''f{{nbhyph}}number⋅meters''.}}<!--

 --><ref>The style for expressing guide numbers throughout the metric-observing world is typified by the practices of Metz mecatecheh GmbH, as exemplified by the German-language version of their website for their ''mecablitz 76 MZ-5 digital'' ([https://www.metz-mecatech.de/de/aufnahmelicht/blitzgeraete/spezialblitzgeraete/mecablitz-76-mz-5-digital/ausstattung/ausstattung.html?mobile=1%27a%3D0%27A%3D0%27%27A%3D0 product page specifications here]):<!--

-->{{Quote frame|'''Blitzleistung'''<br />• Hohe max. Leitzahl 76 bei ISO 100/21° und 105 mm}}

This translates to English as follows:

{{Quote frame|'''Flash output'''<br />• High max. guide number 76 at ISO 100/21° and 105 mm}}</ref><!--

NOTE TO EDITORS: REGARDING SPELLING "METERS" VS "METRES", PER WP:ENGVAR (A POLICY INTENDED TO REDUCE EDIT WARRING), there is no valid reason for editors to change the English-variety spelling of words within an article without "substantial reason" and with few exceptions (e.g., when a topic has strong national ties or a term/spelling carries less ambiguity).

--> As such, guide numbers can be reduced either to distance in meters or to f{{nbhyph}}stops depending on how one uses the guide number in a calculation.

In the U.S. however, photographers typically measure distances in [[Foot (unit)|feet]] and require guide numbers scaled accordingly. To serve the U.S. market, manufacturers of flash devices typically provide foot-based guide numbers and add nomenclature such as '''feet''', '''ft''', or the [[Prime (symbol)|foot symbol]] (<small>&thinsp;</small>′&thinsp;) to unambiguously denote that fact, e.g. '''Guide number: 92′'''.<!--

--><ref>One example of using the [[Prime (symbol)|single-prime]] (foot symbol) when marketing in the U.S. is as practiced by Bolt, which specifies the guide number of their ''VS&nbsp;510P'' ([http://www.boltflashes.com/detail?sku=750855 product page here]) as follows:<!--

-->{{Quote frame|The '''VS-510P Wireless TTL Shoe Mount Flash''' from '''Bolt''' is a dedicated TTL flash for use with Pentax & Samsung DSLR, mirrorless or point-and-shoot cameras. The VS-510 features a guide number of 141' at ISO 100 and an adjustable tilt head with five positions: 0 to 90°.}}<!--

-->Another notable example of how flash device guide numbers are communicated to the U.S. market is the large retailer, B & H Foto & Electronics ([https://www.bhphotovideo.com/c/search?Ntt=On+Camera+Flashes&N=0 on-camera flash page here]), which states guide numbers formatted like this example for Nissin's ''i60A'':<!--

-->{{Quote frame|• Guide Number: 197' at ISO 100 and 200mm}}</ref><!--

--><ref group=note>Bold typestyle is not a required convention for denoting guide numbers. Bolding is consistently used throughout this article to unambiguously distinguish the text and measures being discussed.</ref> Another common practice when flash devices are marketed in the U.S. is to provide ''two'' guide numbers—which can be expressed in a variety of formats—so distances and f{{nbhyph}}numbers may be calculated using either feet or meters, e.g. '''Guide number: {{nowrap|30 m<small>&thinsp;</small>/<small>&thinsp;</small>98&nbsp;ft.}}'''<ref name="List" />

Though nomenclature conventions such as these can make guide numbers misleadingly appear to be ''length-based'' units of measure, they serve as ''notations'' to eliminate ambiguity as to which length-based system of measurement underlies the guide numbers. As with metric-based guide numbers, foot-based guide numbers are a two-factor unit of measure except the units are {{nowrap|''f{{nbhyph}}number⋅feet''.}}

To convert a guide number given in meters to feet, divide by 0.3048. To convert a guide number given in feet to meters, ''multiply'' by 0.3048.

=== Calculating with guide numbers ===
It is easy to use guide numbers to calculate either an aperture or a flash-to-subject distance. Consider a flash device with a rating of 28 meters (which might be marked "92 feet", "28 DIN", "28/92", "92", etc.).

Suppose a photographer has a flash device with a guide number of '''44 (m) / 144 (ft)''',<ref group=note>The dual-scale format used for many examples of guide numbers within this article (similar to the practice observed by Metz mecatech GmbH and others) is purely a matter of style. It is used here not only because it is relatively compact, but because by observing the convention of enclosing the symbols for length within parentheses, it is clear they are ''notations as to the measurement system underlying the guide numbers'' and don't misleadingly appear to be units of measure for length with their accompanying numeric magnitudes.</ref> sets the camera's aperture to {{f/|4}}, and wants to know the required flash-to-subject distance; he merely divides the guide number by 4. Thus, a subject 11 meters or 36 feet away will be correctly illuminated {{nowrap|(GN 44 (m) ÷ }}{{f/|4}} = 11 m, and {{nowrap|GN 144 (ft) ÷ }}{{f/|4}} = 36 ft). For the same guide number and an aperture of {{f/|8}}, the light source must be 5.5 meters or 18 feet from the subject.

Alternatively, if one has an established flash-to-subject distance and wants to find the required f-number, one divides the guide number by the distance. Example: '''Guide number = 48                          (m)''' and the distance is 6 meters; one needs and aperture of {{f/|8}} (GN 48 ÷ 6 m = {{f/|8}}).

====Example for finding a distance====
Suppose a photographer wants to shoot with an aperture of {{f/|2.8}} and the guide number is '''28 (m) / 92 (ft)'''. The flash device must be 10 meters (33 feet) from the subject.
:In metric: GN 28 ÷ {{f/|2.8}} = 10 m
:In U.S. customary units: GN 92 ÷ {{f/|2.8}} = 33 ft

====Example for finding an aperture====
Suppose a photographer's flash-to-subject distance is 9.75 meters (32 feet) and the guide number is '''39 (m) / 128 (ft)'''. The aperture must be {{f/|4}}.
:In metric: GN 39 ÷ 9.75 m = {{f/|4}}
:In U.S. customary units: GN 128 ÷ 32 ft = {{f/|4}}

== Details ==
[[File:Sekonic L-358 Flash Master.jpg|thumb|right|220px|An incident-light meter measures the true ''luminous exposure'' (in {{nowrap|lux⋅seconds)}} arriving at a scene.]]<!--

 -->The magnitude of guide numbers is a function of the following four variables:
# The total luminous energy (in [[lumen second|lumen⋅seconds]]) emitted by the flash head (which is itself the product of the duration and the average [[luminous flux]] of a flash). See ''[[#Glossary|Glossary]]'', below for illumination terminology.
# The [[solid angle]] subtended by the circular- or rectangular-profile beam as it leaves the flash head (the average of the beam's X- and Y-axis angles).
# The ISO sensitivity setting.
# Filters (either on the flash or on the camera lens). See ''[[#Effect of filters|Effect of filters]]'', below.

The above variables fall into two classes that influence the magnitude of guide numbers:

# Those that affect the non-distance-related ''intensity'' of a flash arriving at a scene (a property called [[illuminance]], measured in [[lux]]) or its ''duration''; namely its power setting, flash coverage angle, and [[color gel]]s in front of the flash head.
# Those that affect the camera's non-aperture-related ''light sensitivity''; namely [[Photographic filter|lens filters]] and the [[Film speed|ISO rating of the film]]/imaging sensor.

Changing either the f{{nbhyph}}stop or the flash-to-subject distance does ''not'' affect guide numbers because, by definition, choosing a different value for one factor is automatically accompanied by a reciprocal adjustment in the other.

Most modern flash devices can operate at guide numbers less than their maximum ratings via either manual adjustment of their power settings in binned steps, by an in-flash automatic light sensing feature, or by being cued by the camera's sensor; both the latter options make continuously variable adjustments. Manual attenuation settings are usually steps in powers of 0.5 (full f{{nbhyph}}stops) that commonly extend five to eight f{{nbhyph}}stops deep {{nowrap|(power levels of <sup>1</sup>/<sub>2</sub>}}, {{nowrap|<sup>1</sup>/<sub>4</sub>}}, {{nowrap|<sup>1</sup>/<sub>8</sub> .... }}{{nowrap|<sup>1</sup>/<sub>256</sub>).}}<!-->EDITORS: The Canon Speedlite 430EX III-RT goes down to 1/128; the Nikon SB-5000 AF Speedlight goes down to 1/256. THERE IS NO POINT TO ADDING A NOTE OR REFERENCE FOR MATERIAL THAT RAPIDLY CHANGES WITH MODEL NUMBERS.</!--> To calculate how reductions in power levels affect guide numbers, see ''[[#Effect of power settings|Effect of power settings]]'', below.

Shutter speeds do not factor into guide number calculations with electronic flash and, for the most part, have no effect on exposures. See ''[[#Effect of shutter speeds|Effect of shutter speeds]]'', below.

Guide numbers are not affected by scene [[reflectance]]. Guide numbers are a function of the [[illuminance]] and duration of a flash (a property called ''luminous exposure'' that have [[Exposure (photography)#Luminous exposure|lux⋅seconds]] as their units of measure) ''arriving'' at a scene as measured by an incident-light meter (pictured at right), not the amount leaving the scene.<!--

 --><ref name="Scantips" /><!--

 --><ref group=note>Whereas ''scene'' reflectance (the [[albedo]] of the objects being photographed) have no influence on the illuminance (lux value) arriving at any given scene, reflective surfaces ''along the path'' between a flash device and a scene, such as light-colored ceilings, do have an influence. Guide numbers are often calculated by manufacturers for optimum results in average indoor settings. See ''Characterizing the Output of Photographic Flash Units'', by Douglas A. Kerr ([http://dougkerr.net/Pumpkin/articles/Photoflash_Output.pdf PDF here]) for more.</ref><!--

 --> This often seems counterintuitive to hobbyists who incorrectly assume that cameras' built-in reflected-light meters are a definitive measure of exposure. However, this principle underlies why using a camera with a through-the-lens meter to photograph a park bench surrounded by sunlit snow underexposes the image, making the bench appear nearly black and the snow as dark as grass and foliage. This is because reflected-light meters are calibrated for an average scene reflectance of 18 percent and can't "know" <!-- EDITORS REGARDING QUOTE MARKS: The quote marks around "know" are not "scare quotes". They are to highlight and convey that the term of common-vernacular (know) is not a literal and technically correct meaning. -->when a scene has non-average reflectance. See also ''[[Gray card]]'' and ''[[Light meter]]''.<!-- EDITORS: YES, THIS IS TRUE AND IS A BASIC PART OF PHOTOGRAPHY 101. *PLEASE* CAREFULLY STUDY THE CITATION AND THE "LIGHT METER" ARTICLE BEFORE SUCCUMBING TO THE TEMPTATION TO REWRITE THIS PARAGRAPH. BUILT-IN REFLECTED-LIGHT METERS IN CAMERAS ONLY WORK BECAUSE THEY ASSUME AN AVERAGE REFLECTANCE OF 18%. IF YOU HAVE A SCENE WITH HIGH REFLECTANCE—LIKE SNOW—THEN REFLECTED-LIGHT METERS WILL PRODUCE WILDLY UNDEREXPOSED PHOTOS WHEREAS INCIDENT-LIGHT METERS (MEASURING THE LIGHT HEADING TOWARDS THE SUBJECT) WILL YIELD PROPER EXPOSURES. DO YOU REMEMBER SEEING PROS IN STUDIOS USING HAND-HELD INCIDENT-LIGHT METERS HELD NEAR A MODEL? THAT'S FOR A REASON. BUILT-IN REFLECTED-LIGHT METERS IN CAMERAS ARE MERELY A (VERY) HANDY CONVENIENCE BUT THEY ARE FAR FROM THE PROPER WAY TO MEASURE LIGHT IN PHOTOGRAPHY. IN FACT, THAT'S WHY CAMERAS GENERALLY ALLOW YOU TO ADJUST EXPOSURES ±3 EV: TO COMPENSATE FOR NON-STANDARD REFLECTANCE, LIKE A SPOTLIT ANNOUNCER ON A STAGE WITH A DARK CURTAIN BEHIND HIM. ±3 EV IS A 64:1 RANGE OF UNCERTAINTY IN LIGHT INTENSITY. AS WITH ALL PHOTOGRAPHIC LIGHTING (CONTINUOUS OR FLASH), GUIDE NUMBERS CAN ONLY BE PROPERLY MEASURED BY AN INCIDENT-LIGHT METER MEASURING THE AMOUNT OF AVAILABLE LIGHT (THE AMOUNT HEADING *TOWARDS* THE SCENE).

 -->

Guide number distances are always measured from the ''flash device'' to the subject; if the flash device is detached from the camera, the position of the camera is irrelevant. Furthermore, unless a flash device has an automatic zoom feature that follows the setting of a camera's zoom lens, guide numbers do not vary with the focal length of lenses.

Note that manufacturers of flash devices may provide guide numbers ratings specified relative to ISO 200, which increases them by the square root of the difference, or a 41 percent increase relative to those given at ISO 100.<!--

 --><ref name="ISO200" /> See ''[[#Effect of ISO sensitivity|Effect of ISO sensitivity]]'', below. When comparing or shopping for flash devices, it is important to ensure that the guide numbers are given in the same ISO sensitivity, are for the same coverage angle, and reduce to the same unit of distance (meters or feet). When these three variables have been normalized, guide numbers can serve as a relative measure of intrinsic illuminating energy rather than an inconstant metric for calculating exposures.

== Effect of power settings ==
Most modern electronic flash devices have manually adjustable power settings. Moreover, virtually all modern on-camera flash devices that have manually adjustable power settings also provide either a built-in [[Slide rule#Circular slide rules|mechanical circular calculator]] (such as shown in the photo at the top of this article) or a digital display that automatically shows the effect power levels have on f{{nbhyph}}stop and distance (guide number).

Nevertheless, for those who want to master the math, guide numbers diminish from their full-power ratings as the square root of their fractional setting per the following formula:

:<math>Full\ power\ GN\times\sqrt{{y}/{x}}=Reduced\ power\ GN</math>

:…where
:<math>y</math> is the numerator in the fraction of the power setting
:<math>x</math> is the denominator in the fraction of the power setting

The following is a step-by-step example of using the above formula: Suppose your full-power guide number is '''48''' (it is irrelevant if it is scaled for meters or feet for this purpose) and the flash device is set to {{nowrap|<sup>1</sup>/<sub>16</sub><small>&thinsp;th</small>}} power. Divide 1 by 16 to obtain 0.0625. Take the [[square root]] of that (the <math>\sqrt{x}</math> button on a calculator), which equals 0.25, and multiply that by the guide number of '''48''' to obtain a reduced-power guide number of '''12.0'''.

The mathematical relationship between guide numbers and power levels can also be understood using the below alternative formula, which is suitable whenever the numerator in the fractional power setting is 1 (which is usually the case with flash devices):

:<math>Full\ power\ GN\div\sqrt x =Reduced\ power\ GN</math>

:…where
:<math>x</math> is the denominator in the fraction of the power setting

Example: Suppose your full-power guide number is '''51''' and your flash device is set to {{nowrap|<sup>1</sup>/<sub>32</sub><small>&thinsp;nd</small>}} power. Take the square root of 32 (the <math>\sqrt{x}</math> button on a calculator), which equals approximately 5.657. Divide 51 by 5.657 to obtain a reduced-power guide number of '''9.0'''.

== Effect of flash angle (zoom setting) ==
Many flash devices have auto- or manual-adjust zoom features that permit the illumination angle to be widened (lessening the guide number) to fully illuminate the image area of wide-angle lenses, or narrowed (increasing the guide number) for telephoto lenses. Such coverage angles may be given in degrees but are often expressed as being equivalent to lens focal lengths for [[35mm format|full-frame, 35&nbsp;mm]] cameras. Manufacturers' advertising practices vary as to the angle of coverage underlying their guide number ratings, in large part because some flash devices can be zoomed whereas others are fixed.

Virtually all modern on-camera flash devices with zoomable flash heads also have either a built-in mechanical circular calculator (such as shown in the photo at the top of this article) or a digital display; both automatically show the effect zoom levels have on f{{nbhyph}}stop and distance (guide number).

Nonetheless, when comparing or shopping for flash devices with zoom heads, it would certainly be helpful if it were possible to mathematically convert advertised guide numbers from one manufacturer's flash angle (zoom level) to another manufacturer's flash angle. This is because guide numbers are often—though ''not always''—given at their most zoomed setting and not all flash devices can zoom to the same extent.<ref group=note>Another not-uncommon marketing practice is to rate flash devices for a coverage angle suitable for use with a 35&nbsp;mm-format, full-frame lens with a 35&nbsp;mm focal length (a flash coverage angle of 60° horizontally).</ref>

Unfortunately, the optics of flash heads are complex; each manufacture's designs not only have illumination areas that are slightly different, but are the product of differing relative proportions of transmission, diffusion, reflection, and refraction among their optical elements ([[Flashtube|flash tube]], reflector, [[Fresnel lens]], and add-on wide-angle adapter). Accordingly, there is no universal formula for precisely calculating how guide numbers diminish from, for instance, a 105&nbsp;mm setting to 50&nbsp;mm or 35&nbsp;mm settings. One may consult the users guide for a specific flash device to obtain guide numbers for different zoom settings.

The below table illustrates the variation in guide numbers depending on zoom level for some select, relatively high-power zoom-capable flash devices.

{| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #3E3E3E solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="8" style="background:#3E3E3E; text-align:center"|<span style="color:white;">VARIATION IN DECAY OF GUIDE NUMBER<br />VERSUS FLASH ANGLE (NORMALIZED TO 105&nbsp;mm)<br />WITH SELECTED ZOOM-CAPABLE FLASH DEVICES</span>
|-
|style="background:#d9d9d3; text-align:center"|'''Flash<br /> angle'''<sup>[A]</sup>
|style="background:#d9d9d3; text-align:center"|'''&nbsp;Vivitar&nbsp;<br />285'''
|style="background:#d9d9d3; text-align:center"|'''Sony<br />HVL-F58AM'''
|style="background:#d9d9d3; text-align:center"|'''Yongnuo<br />YN-568EX'''
|style="background:#d9d9d3; text-align:center"|'''Canon<br />430EX III-RT'''
|style="background:#d9d9d3; text-align:center"|'''Nikon<br />SB-900'''
|style="background:#d9d9d3; text-align:center"|'''Metz<br /> 58 AF-2'''
|style="background:#d9d9d3; text-align:center"|'''[[Median]]<br />value'''
|-
|style="background:#d9d9d3; text-align:right"|105&nbsp;mm
|style="text-align:center"|100%
|style="text-align:center"|100%
|style="text-align:center"|100%
|style="text-align:center"|100%
|style="text-align:center"|100%
|style="text-align:center"|100%
|style="text-align:center"|100%
|-
|style="background:#d9d9d3; text-align:right"|50&nbsp;mm
|style="text-align:center"|85.7%
|style="text-align:center"|72.4%
|style="text-align:center"|72.4%
|style="text-align:center"|76.8%
|style="text-align:center"|80.7%
|style="text-align:center"|72.4%
|style="text-align:center"|74%
|-
|style="background:#d9d9d3; text-align:right"|35&nbsp;mm
|style="text-align:center"|71.4%
|style="text-align:center"|62.1%
|style="text-align:center"|67.2%
|style="text-align:center"|65.1%
|style="text-align:center"|68.4%
|style="text-align:center"|60.3%
|style="text-align:center"|66%
|-
|style="background:#d9d9d3; text-align:right"|28&nbsp;mm
|style="text-align:center"|50.0%
|style="text-align:center"|53.4%
|style="text-align:center"|51.7%
|style="text-align:center"|55.8%
|style="text-align:center"|60.6%
|style="text-align:center"|53.4%
|style="text-align:center"|53%
|}
<small>Note A: Flash angle is equivalent to the denoted lens focal length for a full-frame 35&nbsp;mm camera.</small>

== Effect of ISO sensitivity ==
[[File:ISO 12,800 night-time flash.jpg|thumb|right|400px|Particulates and aerosols typically present in outside air limit the extent to which high guide numbers created by high ISO sensitivities can be used to illuminate scenes at long distances.<p>This photo was shot in fair quality air at ISO 12,800 using a modestly powerful camera-mounted flash, yielding a high guide number of '''438&nbsp;(m)<small>&thinsp;</small>/<small>&thinsp;</small>1438&nbsp;(ft)'''. When shot at {{f/|1.8}} to favor distance, the utility pole marked by the arrow would be properly illuminated were it not for haze glare, which fogged the image and diminished brightness.</p>]]<!--
 -->
Among other variables like illumination angle (for devices with zoomable flash heads) and power setting, guide numbers are a function of the ISO sensitivity (film speed or ISO setting on a digital camera). Guide numbers change as the square root of the difference in ISO sensitivity. Accordingly, a greater ISO sensitivity yields a greater guide number.

To allow photographers to properly calculate exposures, even older, base-model flash devices have at least a tabular table on the device showing its guide number for a limited range of common ISO sensitivities. Today, the state of the art has advanced so that with the exception of the least expensive models, virtually all modern on-camera flash devices feature either a built-in mechanical circular calculator (such as shown in the photo at the top of this article) or—more modern yet—a digital display; both methods automatically calculate the effect ISO settings have on f{{nbhyph}}stop and distance (guide number). Such features make it exceedingly easy to find a suitable combination of f{{nbhyph}}stop and distance so photographers seldom need to concern themselves with the mathematical details underlying how their flash devices' guide number changes with different ISO sensitivities.

Still, it can be helpful when comparing flash devices to understand how guide numbers vary with ISO sensitivity. Usually manufacturers state their products' guide number ratings relative to an ISO sensitivity of 100. However, some manufacturers of flash devices may provide guide numbers ratings specified relative to ISO&nbsp;200, which increases its guide number by 41 percent relative to those given at ISO&nbsp;100.<!--

 --><ref name="ISO200" /><!--

 -->

The below table shows the proportional change in a flash device's guide number relative to both ISO&nbsp;100 and ISO&nbsp;200.

Note that the extremely high guide numbers shown in the right-hand portion of the table have a limited real-world ability to extend flash distances. As the above photo illustrates, the ''f{{nbhyph}}number × distance'' reciprocal relationship breaks down when on-camera flash devices that are set to full or near-full power are used in combination with cameras set to very high ISO sensitivities and large apertures (exceedingly long distances). ISO settings like 102,400 can yield guide numbers in excess of '''1220 (m)<small>&thinsp;</small>/<small>&thinsp;</small>4000 (ft)''' that seldom if ever permit extremely long-range flash photography due to particulates and aerosols typically present in outside air that fog images with haze glare and attenuate the reach of the light. Except in unusual atmospheric conditions, extraordinarily large guide numbers will produce suitable results only by either positioning the flash device off-axis from the camera by a fair distance or by shooting at the smallest apertures.

{| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #52524d solid; border-collapse: collapse; font-size: 95%;"
|-
|colspan="25" style="background:#3E3E3E; text-align:center"|<span style="color:WHITE;">'''CHANGE IN GUIDE NUMBERS AS ISO SENSITIVITY VARIES FROM AN ADVERTISED RATING'''</span>
|-
|style="background:#B5B5B5; text-align:right"|'''ISO sensitivity'''<sup>[B]</sup>
|style="background:#C0C0C0; text-align:center"|'''32'''
|style="background:#C0C0C0; text-align:center"|'''40'''
|style="background:#C0C0C0; text-align:center"|'''50'''
|style="background:#C0C0C0; text-align:center"|'''64'''
|style="background:#C0C0C0; text-align:center"|'''80'''
|style="background:#C0C0C0; text-align:center"|'''100'''
|style="background:#C0C0C0; text-align:center"|'''125'''
|style="background:#C0C0C0; text-align:center"|'''160'''
|style="background:#C0C0C0; text-align:center"|'''200'''
|style="background:#C0C0C0; text-align:center"|'''250'''
|style="background:#C0C0C0; text-align:center"|'''320'''
|style="background:#C0C0C0; text-align:center"|'''400'''
|style="background:#C0C0C0; text-align:center"|'''500'''
|style="background:#C0C0C0; text-align:center"|'''640'''
|style="background:#C0C0C0; text-align:center"|'''800'''
|style="background:#C0C0C0; text-align:center"|'''1600'''
|style="background:#C0C0C0; text-align:center"|'''3200'''
|style="background:#C0C0C0; text-align:center"|'''6400'''
|style="background:#C0C0C0; text-align:center"|'''12,800'''
|style="background:#C0C0C0; text-align:center"|'''25,600'''
|style="background:#C0C0C0; text-align:center"|'''51,200'''
|style="background:#C0C0C0; text-align:center"|'''102,400'''
|style="background:#C0C0C0; text-align:center"|'''204,800'''
|style="background:#C0C0C0; text-align:center"|'''409,600'''
|-
|style="background:#B5B5B5; text-align:right"|'''Proportional change in GN relative to ISO&nbsp;100'''
|style="background:#DCDCDC; text-align:center"|0.561
|style="background:#dcdcdc; text-align:center"|0.630
|style="background:#dcdcdc; text-align:center"|0.707
|style="background:#dcdcdc; text-align:center"|0.794
|style="background:#dcdcdc; text-align:center"|0.891
|style="background:#dcdcdc; text-align:center"|1.00
|style="background:#dcdcdc; text-align:center"|1.12
|style="background:#dcdcdc; text-align:center"|1.26
|style="background:#dcdcdc; text-align:center"|1.41
|style="background:#dcdcdc; text-align:center"|1.59
|style="background:#dcdcdc; text-align:center"|1.78
|style="background:#dcdcdc; text-align:center"|2.00
|style="background:#dcdcdc; text-align:center"|2.24
|style="background:#dcdcdc; text-align:center"|2.52
|style="background:#dcdcdc; text-align:center"|2.83
|style="background:#dcdcdc; text-align:center"|4.00
|style="background:#dcdcdc; text-align:center"|5.66
|style="background:#dcdcdc; text-align:center"|8.00
|style="background:#dcdcdc; text-align:center"|11.3
|style="background:#dcdcdc; text-align:center"|16.0
|style="background:#dcdcdc; text-align:center"|22.6
|style="background:#dcdcdc; text-align:center"|32.0
|style="background:#dcdcdc; text-align:center"|45.3
|style="background:#dcdcdc; text-align:center"|64.0
|-
|style="background:#B5B5B5; text-align:right"|'''Proportional change in GN relative to ISO&nbsp;200'''
|style="background:#DCDCDC; text-align:center"|0.397
|style="background:#dcdcdc; text-align:center"|0.445
|style="background:#dcdcdc; text-align:center"|0.500
|style="background:#dcdcdc; text-align:center"|0.561
|style="background:#dcdcdc; text-align:center"|0.630
|style="background:#dcdcdc; text-align:center"|0.707
|style="background:#dcdcdc; text-align:center"|0.794
|style="background:#dcdcdc; text-align:center"|0.891
|style="background:#dcdcdc; text-align:center"|1.00
|style="background:#dcdcdc; text-align:center"|1.12
|style="background:#dcdcdc; text-align:center"|1.26
|style="background:#dcdcdc; text-align:center"|1.41
|style="background:#dcdcdc; text-align:center"|1.59
|style="background:#dcdcdc; text-align:center"|1.78
|style="background:#dcdcdc; text-align:center"|2.00
|style="background:#dcdcdc; text-align:center"|2.83
|style="background:#dcdcdc; text-align:center"|4.00
|style="background:#dcdcdc; text-align:center"|5.66
|style="background:#dcdcdc; text-align:center"|8.00
|style="background:#dcdcdc; text-align:center"|11.3
|style="background:#dcdcdc; text-align:center"|16.0
|style="background:#dcdcdc; text-align:center"|22.6
|style="background:#dcdcdc; text-align:center"|32.0
|style="background:#dcdcdc; text-align:center"|45.3
|}
<small>Note B: The ISO sensitivities shown in this table are their common nomenclature values; their actual underlying values may be slightly different, such as ISO&nbsp;250, which is actually approximately 252.</small>

== Effect of filters ==
Filters reduce guide numbers regardless of whether they are [[color gel|gels]] placed over the flash device or are lens filters on the camera. Flash devices may come with detachable color-correction gels or filters to match the color of the flash with different types of ambient lighting such as incandescent and fluorescent. Some modern flash devices can even detect when color-correction gels have been attached and automatically compensate for their effect on guide numbers.

Unless a hot shoe-mounted electronic flash device's power can be controlled by a camera via [[through-the-lens metering]] (TTL), guide numbers must be manually compensated for the effect of on-lens filters.<ref group=note>Even with TTL, non-average scenery such as off-center subjects with distant backgrounds or scenery with elements that have non-average reflectance can confound TTL metering. However, such situations cannot confound guide number equations.</ref> For instance a typical [[Polarizing filter (photography)|polarizing filter]], which attenuates 1–1.5 f{{nbhyph}}stops, will diminish guide numbers to 71–60% of their unfiltered rating.

Guide numbers diminish as the square root of filter attenuation in f{{nbhyph}}stops, as per the following formula:

:<math>GN\times\sqrt{0.5^{n}}=Filtered\ GN</math>

:…where <math>n</math> equals the filter's rated loss in f{{nbhyph}}stops.

The following is a step-by-step example of using the above formula: Suppose your guide number is '''32''' (it is irrelevant if it is scaled for meters or feet for this purpose) and the rated filter loss is 1.5 f{{nbhyph}}stops. Take 0.5 and [[Exponentiation|raise it to the power]] of 1.5 (using the <math>x^y</math> button on a scientific calculator), which equals roughly 0.35355. Take the [[square root]] of that (the <math>\sqrt{x}</math> button), which equals approximately 0.595, and multiply that by the guide number of '''32''' to obtain a filtered guide number of '''19.0'''.

The below table provides some common filter values.

{|border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #3E3E3E solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="4" style="background:#3E3E3E; text-align:center"|<span style="color:white;">ATTENUATION OF<br />GUIDE NUMBERS<br />WITH FILTER LOSS</span>
|-
|style="background:#d9d9d3; text-align:center"|'''f-stop<br />loss'''
|style="background:#d9d9d3; text-align:center"|'''Factor'''
|style="background:#d9d9d3; text-align:center"|'''f-stop<br />loss'''
|style="background:#d9d9d3; text-align:center"|'''Factor'''
|-
|style="text-align:center"|'''<sup>1</sup>/<sub>3</sub>'''
|style="text-align:center"|89.1%
|style="text-align:center"|'''1<sup>2</sup>/<sub>3</sub>'''
|style="text-align:center"|56.1%
|-
|style="text-align:center"|'''<sup>1</sup>/<sub>2</sub>'''
|style="text-align:center"|84.1%
|style="text-align:center"|'''2'''
|style="text-align:center"|50.0%
|-
|style="text-align:center"|'''<sup>2</sup>/<sub>3</sub>'''
|style="text-align:center"|79.4%
|style="text-align:center"|'''2<sup>1</sup>/<sub>3</sub>'''
|style="text-align:center"|44.5%
|-
|style="text-align:center"|'''1'''
|style="text-align:center"|70.7%
|style="text-align:center"|'''2<sup>1</sup>/<sub>2</sub>'''
|style="text-align:center"|42.0%
|-
|style="text-align:center"|'''1<sup>1</sup>/<sub>3</sub>'''
|style="text-align:center"|63.0%
|style="text-align:center"|'''2<sup>2</sup>/<sub>3</sub>'''
|style="text-align:center"|39.7%
|-
|style="text-align:center"|'''1<sup>1</sup>/<sub>2</sub>'''
|style="text-align:center"|59.5%
|style="text-align:center"|'''3'''
|style="text-align:center"|35.4%
|}

When a flash device is set to manual (M) or automatic (A) exposure mode and is not being controlled via the camera's through-the-lens metering, a convenient way to compensate for the effect of a lens-mounted filter is to set the ISO rating on a camera to a higher value than the flash device. For instance, if a polarizing filter attenuates by 1 f{{nbhyph}}stop and the flash device is set to ISO&nbsp;100, then the camera can simply be set to ISO&nbsp;200. The extra camera sensitivity compensates for the loss due to the filter.

The formula governing this relationship is as follows:

:<math>Flash\ ISO\times2^{n}=Camera\ ISO</math>

:…where <math>n</math> equals the camera filter's rated loss in f{{nbhyph}}stops.

Here is a step-by-step example of using this formula: Suppose a filter attenuates by 1<sup>1</sup>/<sub>3</sub> f{{nbhyph}}stops and the flash device is set to ISO&nbsp;100. Take 2 and raise it to the power of 1.3333 (using the <math>x^y</math> button on a scientific calculator), which is approximately 2.5198, and then multiply that by 100, which equals about 252. The nearest standard camera setting is ISO&nbsp;250.

== Effect of shutter speeds ==
[[File:Flash sync failure.jpg|thumb|right|240px|With focal-plane shutters, exposures faster than the X-sync speed can cause the image area to be partially obscured by the closing curtain during the flash.]]
[[File:E. Leitz Wetzlar flash - 1.JPG|thumb|right|240px|A Leica "CEYOO"-model flashgun with folding reflector (1950–1959), which accepted "Midget" {{nowrap|No.&thinsp;5}} flashbulbs. The blue coating (type 5B) permitted use with color film.]]
[[File:GE-Synchro-Press-No.11.svg|thumb|right|460px|The photometric<!-- EDITORS: PLEASE DO NOT LINK “PHOTOMETRIC”. OUR ARTICLE DOES NOT COVER THE MOST COMMON WAY THE TERM IS USED (MEASURING TIME VS INTENSITY) --> output of the GE Synchro-Press {{nowrap|No.&thinsp;11}} flashbulb is shown here. Like all Class M (medium peak) bulbs, its peak output was defined as occurring 20 milliseconds after applying electrical current. The {{nowrap|No.&thinsp;11}} had a peak luminous flux of 1.8 million lumens. Its rated luminous energy, ''Q''<sub>v</sub> of 23,000 lumen⋅seconds is the shaded area to the right of the definitional shutter opening point ({{nowrap|<sup>1</sup>/<sub>800</sub><small>&thinsp;th</small>}} of a second before the point of peak luminous flux).]]
=== With electronic flash ===
When electronic flash devices based on [[flashtube]] technology are used with most modern cameras (those with [[focal-plane shutter]]s), shutter speed has no effect on guide numbers.<ref group=note>A notable exception to this generality is when a flash device at full power is used in combination with cameras equipped with leaf shutters set to very brief exposure times.</ref> See also ''[[Shutter (photography)]]''.

This is because even at the most powerful settings, flash durations seldom exceed a few milliseconds (thousandths of a second). With focal-plane shutters, a flash begins shortly after the shutter curtain has fully opened and must extinguish before the curtain begins to close. Selecting any shutter speed faster than the camera's rated X{{nbhyph}}sync speed, which is often between {{nowrap|<sup>1</sup>/<sub>60</sub><small>&thinsp;th</small>}} and {{nowrap|<sup>1</sup>/<sub>200</sub><small>&thinsp;th</small>}} of a second (from as long as 16.7 milliseconds to as little as 5.0 milliseconds) causes the shutter curtain to begin wiping closed across the film or sensor before the flash has extinguished. When this happens, an underexposed, gradated band appears along an edge of the image—often trailing off darker towards the left or bottom, as seen in the photo at top right.<!-->EDITORS: REMEMBER THAT THE LENS REVERSES THE IMAGE HORIZONTALLY AND VERTICALLY, SO TOP-TO-BOTTOM CURTAINS CUTS OFF THE BOTTOM OF THE IMAGE.</!-->

Conversely, longer exposures also have no effect on guide number. After the flash has extinguished, longer shutter speeds will only increase the contribution from continuous ambient light, which can lead to ghosting with moving subjects. See also ''[[Flash synchronization]]''.

=== With flashbulbs ===
Shutter speeds ''used to'' (and still do today) influence guide numbers when using [[Flash (photography)#Flashbulbs|flashbulbs]] due to their relatively long flash durations. Vintage flashbulbs, though no longer made, are still available and have a niche following, largely because even medium-size bulbs such as the once-popular General Electric Synchro-Press {{nowrap|No.&thinsp;11}} had huge light outputs on the order of 23,000 lumen⋅seconds—far exceeding the most powerful of today's hot shoe-mounted electronic flash devices. At a relatively slow shutter speed of {{nowrap|<sup>1</sup>/<sub>25</sub><small>&thinsp;th</small>}} of a second (40 milliseconds), the GE {{nowrap|No.&thinsp;11}} had a guide number of '''97.5 (m)<small>&thinsp;</small>/<small>&thinsp;</small>320&nbsp;(ft)''' at ISO 100 when using a typical 6- or 7-inch-diameter (150–175&nbsp;mm) polished reflector.<ref>[http://www.flashbulbs.com/ Flashbulbs.com]: [http://www.flashbulbs.com/flash_info.htm "Flash info"]</ref> With peak powers often between one and two million lumens, many young [[baby boomers]] chased after fairylike retinal bleached spots (a symptom of [[flash blindness]]) for minutes after having their pictures taken at close distance with flashbulbs of the era.

If one wanted the benefit of all the light produced by a flashbulb (highest possible guide number), relatively long exposure times were required because most flashbulbs didn't stop producing useful amounts of light until 20–90 milliseconds (ms) after electrical current was applied. The GE {{nowrap|No.&thinsp;11}} flashbulb for instance, was a Class M (medium peak) bulb, which were designed to produce peak luminous fluxes 20&nbsp;ms after firing (see the graph at lower right). The {{nowrap|No.&thinsp;11}} was intended for [[Shutter (photography)|leaf shutter]]-type cameras and [[Flash synchronization|M&nbsp;sync]] photoflash triggering, which gave M bulbs a head start by delaying the opening of the shutter so any given camera's fastest exposure time would be centered at the 20&nbsp;ms point (an 18.75&nbsp;ms delay for instance, for a definitional camera capable of {{nowrap|<sup>1</sup>/<sub>400</sub><small>&thinsp;th</small>}} second exposures, or 2.5&nbsp;ms).<!--

 --><ref group=note>During the heyday of flashbulbs (post-WWII to the late 1960s), adjustment tolerances for the sync timing of camera shutters varied; each manufacturer had their own specifications and tolerances. Though ''definitional specifications'' could be expressed to arbitrary precision such as hundredths of a millisecond (tens of microseconds), practical manufacturing with mechanical shutters did not have such [[Accuracy and precision|accuracies and precisions]]. By the 1980s, when exceedingly few serious hobbyists or professionals were still using flashbulbs, some camera repair centers had very loose adjustment specifications for consumer-grade cameras, such as {{nowrap|15–22&nbsp;ms}} for M&nbsp;sync, which averaged 18.5&nbsp;ms. Manufacturers of professional studio cameras like [[Hasselblad]] and [[press camera]]s like [[Graflex]] had tighter sync timing tolerances during the flashbulb era because their cameras were used by demanding professionals in disciplines where there was often significant economic consequences to underexposures with flashbulbs at fast shutter speeds.</ref><!--

 -->  The GE {{nowrap|No.&thinsp;11}} stopped producing useful amounts of light roughly 50&nbsp;ms after current was applied. Thus, a camera with a fastest shutter speed of {{nowrap|<sup>1</sup>/<sub>400</sub><small>&thinsp;th</small>}} of a second (one that began exposures 18.75&nbsp;ms after a bulb was fired with M sync triggering), and which was set to {{nowrap|<sup>1</sup>/<sub>25</sub><small>&thinsp;th</small>}} of a second, would close its shutter 59&nbsp;ms after triggering a flashbulb (18.75&nbsp;ms&thinsp;+&thinsp;40&nbsp;ms&nbsp;=&nbsp;58.75&nbsp;ms) and would achieve the maximum rated guide number from the {{nowrap|No.&thinsp;11}}.

So long as one used flashbulbs with leaf shutter-type cameras, faster exposures and larger apertures could be used to minimize motion blur or reduce [[depth of field]] at the expense of guide number. In the case of the GE Synchro-Press {{nowrap|No.&thinsp;11}} with M&nbsp;sync for instance, shutter speeds as long as {{nowrap|<sup>1</sup>/<sub>50</sub><small>&thinsp;th</small>}} of a second still diminished its guide number, though it still managed an impressive '''140&nbsp;(ft)''' at a {{nowrap|<sup>1</sup>/<sub>400</sub><small>&thinsp;th</small>}} second exposure. This relationship between shutter speed and guide number was reflected in the guide number tables printed on flashbulb packaging after the industry-wide adoption of the guide number system, as exemplified by the below-left table for the {{nowrap|No.&thinsp;11}}.

{| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #3E3E3E solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="6" style="background:#3E3E3E; text-align:center"|<span style="color:white;">EFFECT OF SHUTTER SPEED ON GUIDE NUMBER<br />FOR THE GE SYNCHRO-PRESS #11 FLASHBULB<br />(6- OR 7-INCH POLISHED RELFECTOR,<br />M SYNC, ISO 100)</span>
|-
|style="background:#d9d9d3; text-align:left"|'''Shutter<br />speed (s)'''
|style="background:#d9d9d3; text-align:center"|≥'''<sup>1</sup>/<sub>25</sub><small>th</small>'''
|style="background:#d9d9d3; text-align:center"|'''<sup>1</sup>/<sub>50</sub><small>th</small>'''
|style="background:#d9d9d3; text-align:center"|'''<sup>1</sup>/<sub>100</sub><small>th</small>'''
|style="background:#d9d9d3; text-align:center"|'''<sup>1</sup>/<sub>200</sub><small>th</small>'''
|style="background:#d9d9d3; text-align:center"|'''<sup>1</sup>/<sub>400</sub><small>th</small>'''
|-
|style="background:#d9d9d3; text-align:left"|'''Guide<br />number (ft)'''
|style="text-align:center"|320
|style="text-align:center"|260
|style="text-align:center"|250
|style="text-align:center"|190
|style="text-align:center"|140
|}

Cameras with focal-plane shutters—even if they had PC connectors with X, F, M, or S-sync delays ("xenon sync" with zero delay and flashbulbs with peak delays of 5, 20, and 30&nbsp;ms)—could not be used at speeds that attenuated guide numbers with most types of flashbulbs because their light curves were characterized by rapid rise and fall rates; the second shutter curtain would begin wiping shut during a period of rapid change in scene illuminance, causing uneven exposure across the image area that varied in nature depending on exposure duration and the type of bulb. With the GE Synchro{{nbhyph}}Press {{nowrap|No.&thinsp;11}} for instance, a modern camera with a focal-plane shutter and X sync would require a shutter speed of {{nowrap|<sup>1</sup>/<sub>15</sub><small>&thinsp;th</small>}} of a second (67&nbsp;ms) to obtain an even exposure across the entire image area—and a not-insignificant boost in the guide number by capturing all the luminous energy to the left of the 20&nbsp;ms peak.

A notable exception to this limitation with focal-plane shutters was when using FP sync in combination with "flat peak" (FP) bulbs, which had {{nowrap|19–20&nbsp;ms}} rise times followed by broad, relatively level plateaus in their light output curves. The FP bulbs, like GE's {{nowrap|No.&thinsp;6}}, allowed extraordinary flexibility with shutter speeds, ranging from the slowest speeds on the dial to the fastest where only a narrow slit passed over the film—at the expense of course, of guide number.

== Fill flash: Guide numbers vs. distance ==
When [[Fill flash|filling in shadows]] outdoors, powerful flash devices (those with inherently greater guide numbers when compared at the same ISO sensitivity and coverage angle) can be useful because they permit photographers to increase the maximum flash-to-subject distance, such as when taking group photos. Clearly, more power helps because the sun is such a bright, unadjustable light source against which a flash device must compete. However, a contributing factor is that many modern cameras with [[focal-plane shutter]]s can sync with flash devices at speeds no faster than {{nowrap|<sup>1</sup>/<sub>60</sub><small>&thinsp;th</small>}} of a second; such a relatively long exposure requires particularly small apertures and/or low ISO sensitivities, both of which constrain how far a camera and its on-camera flash can be from the subject.

The tables below show the distances at which deep shadows will be filled with one f{{nbhyph}}stop less than the sunlit portions of the scene, which is a common fill level. The exposures given here assume average frontlit subjects under bright or hazy sun with distinct shadows for photos taken between 2 hours after sunrise and 2 hours before sunset.<ref group=note><!--

-->'''The continuous-light portion of fill-flash photos'''<br />
The continuous-light exposures underlying the above tables are in accordance with Eastman Kodak Company's guidelines for exposing film. For example, as exemplified by the technical data sheet for their Kodak Professional Ektar 100 film ([http://imaging.kodakalaris.com/sites/prod/files/files/products/e4046_ektar_100.pdf PDF&nbsp;here]), scenes that are lit by bright or hazy sun with distinct shadows and which are shot between 2 hours after sunrise and 2 hours before sunset are an [http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx illuminance of 40,960 lux] {{Webarchive|url=https://web.archive.org/web/20170814220607/http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx |date=2017-08-14 }} (EV&nbsp;14 @ ISO&nbsp;100). For this illuminance, Kodak recommends settings (ISO&nbsp;100, {{f/|11}}, {{nowrap|<sup>1</sup>/<sub>125</sub><small>&thinsp;th</small>}} of a second) that equal a luminous exposure of {{nowrap|328 lux⋅seconds}}.

This exposure level applies proportionally across the full gamut of Kodak's color and [[Panchromatic film|panchromatic B&W films]] where—at 40,960 lux and {{f/|11}}—a film speed of ISO&nbsp;200 is properly exposed when a scene receives a luminous exposure of {{nowrap|164 lux⋅seconds}}, ISO&nbsp;400 requires {{nowrap|82 lux⋅seconds}}, and so forth.

Kodak's guidance for a proper continuous-light exposure for all film speeds, scene illuminance, and camera settings reduces as follows:
<!--

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[[Special:PermanentLink/797661834#cite note-15]]

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:<math>{\frac{E_v\cdot t\cdot S}{f^2}}=k</math>

:…where,
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''E<sub>v</sub>''</span> is scene [[illuminance]] in [[lux]] (e.g. '''40,960'''; '''81,900'''; and [[Daylight#Intensity in different conditions|'''111,000''']]). A table of lux values vs. EV @ ISO 100 is available [http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx here, by Sekonic.] {{Webarchive|url=https://web.archive.org/web/20170814220607/http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx |date=2017-08-14 }} {{Webarchive|url=https://web.archive.org/web/20170814220607/http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx |date=2017-08-14 }}<!-- EDITORS: WE DON'T WANT TO LINK TO LUX VERSUS EV TABLES ON THE PROJECT BECAUSE THEY ARE NOT STABLE AND VARY WITH THE EDITORIAL TIDES. SEKONIC MAKES PROFESSIONAL-GRADE LIGHT METERS AND THEIR TABLES ARE AUTHORITATIVE AND STABLE. -->
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''t''</span> is exposure time in seconds (e.g. '''0.008''' for {{nowrap|<sup>1</sup>/<sub>125</sub><small>&thinsp;th</small>}} of a second)
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''S''</span> is ISO arithmetic speed or sensitivity (e.g. '''100''', '''200''', and '''400''')
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''f''</span> is the f-number (e.g. '''8''' for an f{{nbhyph}}stop of {{f/|8}}. Common f{{nbhyph}}stops from the <math display="inline">{\sqrt{2}}^{\ n}</math> series include {{f/|1.1892}}, {{f/|1.4142}}, {{f/|2}}, {{f/|2.8284}}, {{f/|4}}, {{f/|5.6569}}, {{f/|8}}, {{f/|11.3137}}, {{f/|16}}, {{f/|22.6274}}, and {{f/|32}})
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''k''</span> is a constant equaling '''256'''

When utilizing fill flash, where balancing flash and continuous light can be difficult, the following four derivatives of this continuous-light exposure equation can be useful:
{{div flex row|justify-content=space-evenly|gap=2em}}
<div><math>{\sqrt{\frac{E_v\cdot t\cdot S}{k}}}=f</math></div>
<div><math>{\frac{{f^2}\cdot {k}}{E_v\cdot t}}=S</math></div>
<div><math>{\frac{{f^2}\cdot {k}}{t\cdot S}}=E_v</math></div>
<div><math>{\frac{{f^2}\cdot {k}}{E_v\cdot S}}=t</math> (take {{sfrac|1|<span style="font-style:italic;font-family:Georgia,serif;font-size: 133%">t</span>}} to obtain the denominator of the fractional shutter speed)</div>
{{div flex row end}}

For any combination of lighting, film, and camera settings that conforms to one of the above five equations, a proper luminous exposure is calculated as follows:
:<math>E_v\cdot t=H_v</math>

:…where,
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''E<sub>v</sub>''</span> is scene [[illuminance]] in [[lux]] (e.g. '''40,960'''; '''81,900'''; and '''111,000''')
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''t''</span> is exposure time in seconds (e.g. '''0.008''' for {{nowrap|<sup>1</sup>/<sub>125</sub><small>&thinsp;th</small>}} of a second)
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''H<sub>v</sub>''</span> is luminous exposure in lux⋅seconds
----
<p style="line-height:70%">&nbsp;</p>
Note that Kodak's exposure guidelines—for photographs taken in typical settings without the benefit of incident-light meters—are for pictures shot during a broad portion of the day with even some light haze in the sky; this is half as bright as the clear-sky, near-noon, open-area, "[[Sunny 16 rule|sunny {{f/|16}} rule]]", which is EV&nbsp;15 at ISO&nbsp;100, or 81,900 lux. Notwithstanding differences in the assumed daylight illuminance, a proper continuous-light exposure is still governed by the same mathematical relationship where <span style="font-style:roman;font-family:Georgia,serif">(''E<sub>v</sub>⋅t⋅S'')''/f''<sup>&thinsp;2</sup>&thinsp;=&thinsp;''k''</span>.

'''Flash exposures vs. continuous-light exposures'''<br />
Importantly, Eastman Kodak Company's exposure recommendations for ''electronic flash'' are slightly different from those for continuous-light exposures. Kodak calculates exposures for electronic flash devices according to the following formula:

----
:<math>GN=\sqrt{\frac{BCPS\times ISO}{20}}</math>

:…where,
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''GN''</span> is guide number
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''BCPS''</span> is beam candlepower seconds
:<span style="font-size:130%;font-style:italic;font-family:Georgia,serif">''ISO''</span> is ISO arithmetic speed or sensitivity (e.g. 100, 200, and 400)

See ''Characterizing the Output of Photographic Flash Units'', by Douglas A. Kerr ([http://dougkerr.net/Pumpkin/articles/Photoflash_Output.pdf PDF here]) for more.
----
<p style="line-height:20%">&nbsp;</p>
This formula means that under the same conditions used above for Kodak Professional Ektar 100 film (ISO&nbsp;100 and {{f/|11}}), a proper ''electronic flash'' exposure equals only {{nowrap|270 lux⋅seconds}} (one [[candlepower]] equals 0.981 [[candela]], which equals 0.981 lux⋅second at a distance of one meter). This slightly reduced flash exposure (versus the continuous-light value of {{nowrap|328 lux⋅seconds}}) compensates for reflections off light colored ceilings, which is typical for indoor flash photography.

'''Outdoors mixing of continuous-light and GN-based fill flash'''<br />
This all means that in ''outdoor'' settings, flash devices must be roughly nine-percent closer {{nowrap|<math display="inline">(\sqrt{270/328}=90.7\%)</math>}} than their indoor-rated guide numbers indicate in order to obtain a full-rated luminous exposure. The above fill-flash tables give distances that have been adjusted accordingly.

Also bear in mind that the distances given in the above tables do not obey the ''f{{nbhyph}}number × distance'' formula when using the f{{nbhyph}}stops shown in the first column because the fill-flash contribution is one f{{nbhyph}}stop less than the sunlit portions of the scene—a 50% underexposure. The values may be correctly calculated by hand when the apertures shown in the first column are larger (numerically smaller f{{nbhyph}}number) by one f{{nbhyph}}stop. Those larger apertures, when expressed in industry-standard nomenclature, are {{f/|11}}, {{f/|8}}, {{f/|6.3}} ({{nowrap|{{f/|5.6}}<small>&thinsp;</small>+⅓)}}, and {{f/|5.6}} but have the following more precise values underlying the above tables: {{f/|11.3137}}, {{f/|8}}, {{f/|6.3496}}, and {{f/|5.6569}} <math display="inline">{(\sqrt{2}}^{\ 7}</math>, <math display="inline">{\sqrt{2}}^{\ 6}</math>, <math display="inline">{\sqrt{2}}^{\ 5\tfrac{1}{3}}</math>, and <math display="inline">{\sqrt{2}}^{\ 5})</math>.</ref>

{| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #3E3E3E solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="16" style="background:#3E3E3E; text-align:center"|<span style="color:white;">—METER BASED—<br />DISTANCE FOR A GIVEN GUIDE NUMBER AT WHICH A FLASH DEVICE CAN<br />FILL SHADOWS TO ONE F{{nbhyph}}STOP LESS THAN THE SUNLIT PORTIONS<br />(SUNLIGHT = EV 14 AT ISO 100, GUIDE NUMBERS AT ISO 100)</span>
|-
|style="background:#d9d9d3; text-align:right"|'''GN (m)'''
|style="background:#d9d9d3; text-align:center"|'''6.5'''
|style="background:#d9d9d3; text-align:center"|'''8'''
|style="background:#d9d9d3; text-align:center"|'''10'''
|style="background:#d9d9d3; text-align:center"|'''12'''
|style="background:#d9d9d3; text-align:center"|'''15'''
|style="background:#d9d9d3; text-align:center"|'''18'''
|style="background:#d9d9d3; text-align:center"|'''22'''
|style="background:#d9d9d3; text-align:center"|'''26'''
|style="background:#d9d9d3; text-align:center"|'''30'''
|style="background:#d9d9d3; text-align:center"|'''36'''
|style="background:#d9d9d3; text-align:center"|'''45'''
|style="background:#d9d9d3; text-align:center"|'''52'''
|style="background:#d9d9d3; text-align:center"|'''60'''
|style="background:#d9d9d3; text-align:center"|'''72'''
|style="background:#d9d9d3; text-align:center"|'''76'''
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>60</sub><small>&thinsp;th</small> @ {{f/|16}}
|style="text-align:center"|0.52 m
|style="text-align:center"|0.64 m
|style="text-align:center"|0.80 m
|style="text-align:center"|0.96 m
|style="text-align:center"|1.20 m
|style="text-align:center"|1.45 m
|style="text-align:center"|1.77 m
|style="text-align:center"|2.09 m
|style="text-align:center"|2.41 m
|style="text-align:center"|2.89 m
|style="text-align:center"|3.61 m
|style="text-align:center"|4.17 m
|style="text-align:center"|4.82 m
|style="text-align:center"|5.78 m
|style="text-align:center"|6.10 m
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>125</sub><small>&thinsp;th</small> @ {{f/|11}}
|style="text-align:center"|0.74 m
|style="text-align:center"|0.91 m
|style="text-align:center"|1.14 m
|style="text-align:center"|1.36 m
|style="text-align:center"|1.70 m
|style="text-align:center"|2.04 m
|style="text-align:center"|2.50 m
|style="text-align:center"|2.95 m
|style="text-align:center"|3.41 m
|style="text-align:center"|4.09 m
|style="text-align:center"|5.11 m
|style="text-align:center"|5.90 m
|style="text-align:center"|6.81 m
|style="text-align:center"|8.17 m
|style="text-align:center"|8.63 m
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>200</sub><small>&thinsp;th</small> @ {{f/|9}} ({{f/|8<small>&thinsp;</small>+⅓}})
|style="text-align:center"|0.93 m
|style="text-align:center"|1.14 m
|style="text-align:center"|1.43 m
|style="text-align:center"|1.72 m
|style="text-align:center"|2.15 m
|style="text-align:center"|2.57 m
|style="text-align:center"|3.15 m
|style="text-align:center"|3.72 m
|style="text-align:center"|4.29 m
|style="text-align:center"|5.15 m
|style="text-align:center"|6.44 m
|style="text-align:center"|7.44 m
|style="text-align:center"|8.58 m
|style="text-align:center"|10.30 m
|style="text-align:center"|10.87 m
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>250</sub><small>&thinsp;th</small> @ {{f/|8}}
|style="text-align:center"|1.04 m
|style="text-align:center"|1.28 m
|style="text-align:center"|1.61 m
|style="text-align:center"|1.93 m
|style="text-align:center"|2.41 m
|style="text-align:center"|2.89 m
|style="text-align:center"|3.53 m
|style="text-align:center"|4.17 m
|style="text-align:center"|4.82 m
|style="text-align:center"|5.78 m
|style="text-align:center"|7.23 m
|style="text-align:center"|8.35 m
|style="text-align:center"|9.63 m
|style="text-align:center"|11.56 m
|style="text-align:center"|12.20 m
|}

{| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #3E3E3E solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="16" style="background:#3E3E3E; text-align:center"|<span style="color:white;">—FOOT BASED—<br />DISTANCE FOR A GIVEN GUIDE NUMBER AT WHICH A FLASH DEVICE CAN<br />FILL SHADOWS TO ONE F{{nbhyph}}STOP LESS THAN THE SUNLIT PORTIONS<br />(SUNLIGHT = EV 14 AT ISO 100, GUIDE NUMBERS AT ISO 100)</span>
|-
|style="background:#d9d9d3; text-align:right"|'''GN (ft)'''
|style="background:#d9d9d3; text-align:center"|'''21'''
|style="background:#d9d9d3; text-align:center"|'''26'''
|style="background:#d9d9d3; text-align:center"|'''33'''
|style="background:#d9d9d3; text-align:center"|'''39'''
|style="background:#d9d9d3; text-align:center"|'''50'''
|style="background:#d9d9d3; text-align:center"|'''60'''
|style="background:#d9d9d3; text-align:center"|'''72'''
|style="background:#d9d9d3; text-align:center"|'''85'''
|style="background:#d9d9d3; text-align:center"|'''100'''
|style="background:#d9d9d3; text-align:center"|'''120'''
|style="background:#d9d9d3; text-align:center"|'''148'''
|style="background:#d9d9d3; text-align:center"|'''170'''
|style="background:#d9d9d3; text-align:center"|'''200'''
|style="background:#d9d9d3; text-align:center"|'''236'''
|style="background:#d9d9d3; text-align:center"|'''250'''
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>60</sub><small>&thinsp;th</small> @ {{f/|16}}
|style="text-align:center"|1.7&nbsp;ft
|style="text-align:center"|2.1&nbsp;ft
|style="text-align:center"|2.6&nbsp;ft
|style="text-align:center"|3.1&nbsp;ft
|style="text-align:center"|4.0&nbsp;ft
|style="text-align:center"|4.8&nbsp;ft
|style="text-align:center"|5.8&nbsp;ft
|style="text-align:center"|6.8&nbsp;ft
|style="text-align:center"|8.0&nbsp;ft
|style="text-align:center"|9.6&nbsp;ft
|style="text-align:center"|11.9&nbsp;ft
|style="text-align:center"|13.6&nbsp;ft
|style="text-align:center"|16.1&nbsp;ft
|style="text-align:center"|18.9&nbsp;ft
|style="text-align:center"|20.1&nbsp;ft
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>125</sub><small>&thinsp;th</small> @ {{f/|11}}
|style="text-align:center"|2.4&nbsp;ft
|style="text-align:center"|3.0&nbsp;ft
|style="text-align:center"|3.7&nbsp;ft
|style="text-align:center"|4.4&nbsp;ft
|style="text-align:center"|5.7&nbsp;ft
|style="text-align:center"|6.8&nbsp;ft
|style="text-align:center"|8.2&nbsp;ft
|style="text-align:center"|9.7&nbsp;ft
|style="text-align:center"|11.4&nbsp;ft
|style="text-align:center"|13.6&nbsp;ft
|style="text-align:center"|16.8&nbsp;ft
|style="text-align:center"|19.3&nbsp;ft
|style="text-align:center"|22.7&nbsp;ft
|style="text-align:center"|26.8&nbsp;ft
|style="text-align:center"|28.4&nbsp;ft
|-
|style="background:#d9d9d3; text-align:right"|&nbsp;<sup>1</sup>/<sub>200</sub><small>&thinsp;th</small> @ {{f/|9}} ({{f/|8<small>&thinsp;</small>+⅓}})
|style="text-align:center"|3.0&nbsp;ft
|style="text-align:center"|3.7&nbsp;ft
|style="text-align:center"|4.7&nbsp;ft
|style="text-align:center"|5.6&nbsp;ft
|style="text-align:center"|7.2&nbsp;ft
|style="text-align:center"|8.6&nbsp;ft
|style="text-align:center"|10.3&nbsp;ft
|style="text-align:center"|12.2&nbsp;ft
|style="text-align:center"|14.3&nbsp;ft
|style="text-align:center"|17.2&nbsp;ft
|style="text-align:center"|21.2&nbsp;ft
|style="text-align:center"|24.3&nbsp;ft
|style="text-align:center"|28.6&nbsp;ft
|style="text-align:center"|33.8&nbsp;ft
|style="text-align:center"|35.8&nbsp;ft
|-
|style="background:#d9d9d3; text-align:right"|<sup>1</sup>/<sub>250</sub><small>&thinsp;th</small> @ {{f/|8}}
|style="text-align:center"|&nbsp;3.4&nbsp;ft&nbsp;<!-- EDITORS: THE NON-BREAKING SPACES ARE SALTED IN SOME OF THIS TABLE TO MAKE IT THE SAME WIDTH -->
|style="text-align:center"|&nbsp;4.2&nbsp;ft&nbsp;<!-- AS THE ONE ABOVE IT WITHOUT THE USE OF CELLPADDING, WHICH PRODUCED UGLY RESULTS -->
|style="text-align:center"|&nbsp;5.3&nbsp;ft&nbsp;<!-- EACH COLUMN IN THE METRIC TABLE CORRESPONDS IN MAGNITUDE TO THE FOOT-BASED ONE. KEEPING -->
|style="text-align:center"|&nbsp;6.3&nbsp;ft&nbsp;<!-- THE TABLES THES SAME WIDTH HELPS WITH THE LESSON WHERE EXAMPLES FROM BOTH TABLES ARE MENTIONED. -->
|style="text-align:center"|&nbsp;8.0&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;9.6&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;11.6&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;13.6&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;16.1&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;19.3&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;23.8&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;27.3&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;32.1&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;37.9&nbsp;ft&nbsp;
|style="text-align:center"|&nbsp;40.1&nbsp;ft&nbsp;
|}
<br />
As can be seen by referring to the above tables, if a photographer has a camera with an X-sync speed of <sup>1</sup>/<sub>125</sub><small>&thinsp;th</small> of a second, is shopping for a flash device, and desires the capability to fill shadows from up to 2.5 meters (8 feet) away, a flash device with a guide number of at least {{nowrap|'''22 (m)<small>&thinsp;</small>/<small>&thinsp;</small>72 (ft)'''}} will be required.

Note that increasing the ISO sensitivity of a digital camera (or choosing a faster film speed) will not increase the distances given in these tables because the extent to which ISO sensitivity affects the exposure in the fill-flash areas of an image ''will equally affect'' the sunlit ones. For any given shutter speed, a flash device can only fill shadows to 50% the contribution from the sun out to a certain distance; at a camera's X{{nbhyph}}sync shutter speed, no change in ISO sensitivity—and accompanying f{{nbhyph}}stop setting—can influence this proportional relationship.

== History ==
[[File:1909 Victor Flash Lamp.jpg|thumb|right|240px|Before the introduction of flashbulbs, photographers used magnesium [[flash powder]] in a [[flash-lamp]]. The pneumatic shutter release cords of the era featured rubber bulbs the photographer squeezed to take a photograph.]]
General Electric introduced the guide number system in 1939 concurrently with the introduction of a compact, wire-filled flashbulb called the {{nowrap|No.&thinsp;5.}}<ref name="Focal" /><ref name="Pop57">''Popular Photography'', May 1957, p. 137</ref><ref name="Minicam">''Minicam'', Vol. 3 (1939), p. 17. Note that the article title on page 20 was "SIMPLIFIED FLASH EXPOSURE TABLES" and, using GE's early terminology, referred to guide numbers as "Flash Numbers" (in title case).</ref> This compelling new way of easily and accurately calculating photoflash exposures was quickly adopted by manufacturers of a wide variety of photographic equipment, including flashbulbs, film, cameras, and flashguns.

The first flashbulb was introduced in 1925 and was filled with [[Flash-lamp|flash powder]]. In 1929, Sashalite Limited in London invented the "Sashalite" flashbulb, which was filled with a crumpled wad of aluminum foil so thin (about one-tenth the width of a human hair) it could not be picked up with fingers.<!--

 --><ref name="Focal">{{cite book|last1=Peres|first1=Michael, R.|title=Focal Encyclopedia of Photography: Digital Imaging, Theory and Applications, History, and Science|date=2007|publisher=Focal Press|isbn=978-0-240-80740-9|edition=4th|page=769}}</ref><ref>''Popular Photography'', April 1938, p. 25</ref><!--

 --> The Sashalite, which was manufactured under contract by General Electric Co., Ltd. in London, came with an instruction sheet directing photographers to insert the Sashalite into "an ordinary electric [[Flashlight|torch]]" and to set their shutter to either "Bulb" or "Time".<!--

 --><ref group=note>[[File:Conley Model C folding camera (circa 1909).png|frameless|right|425px]]When Sashalite's instructions mentioned setting a shutter to its [[Bulb (photography)|"Bulb" setting]], the company was not referring to glass flashbulbs but to ''rubber'' bulbs.  The Sashlite flashbulb was introduced at a time when the equipment typically used for professional indoor portraiture was a large-format studio [[view camera]] and a [[flash-lamp]] with [[flash powder]] in its tray. Advanced hobbyists in 1909—decades before the first flashbulbs—could buy portable [[folding camera]]s, made by Conley Camera Company, from Sears Roebuck for $4.75–$21.50 (equivalent to ${{Inflation|US|5|1909}}–${{Inflation|US|25.10|1914}} in {{CURRENTISOYEAR}}). With the exception of entry-level models, both view-type and folding cameras of this era came with a detachable pneumatic shutter release with a rubber bulb on the end, as seen at right on the $11.75 Model C. With the exception of their entry-level shutter, Conley's shutters—like the Conley Automatic (inset, far right)—had a "B" setting. Though mechanically timed exposures too could be triggered by squeezing the shutter release bulb, "bulb" exposures had the same momentary action as camera shutters have today, as per this description from Sears Roebuck's 1909 ''Cameras [&] Photographic Supplies'', which devoted three pages to the features and operation of Conley's shutters:<!--</span> EDITORS: PLEASE DON'T DELETE THIS END-SPAN. IT'S FIXING A BUG IN SOMETHING ... introduced in Revision as of 04:07, 13 September 2017 (UTC), doesn't seem to be needed anymore, if it ever was -->

<span style="font-style:roman;font-family:Georgia,serif>{{quote|With the indicator set to B, the shutter opens when the bulb is pressed and remains open as long as the pressure is maintained (“bulb” exposure), a very convenient means of making time exposures of only a few seconds' duration.}}</span>

The [[Kodak|Eastman Kodak Company]] sold cameras before the flashbulb era too. Though their entry level consumer cameras came without the option of a pneumatic shutter release, Kodak retained the convention of using "B” on shutters for the momentary actuation setting but referred to it as "Brief Time" in brochures for cameras like their ''Folding Autographic Brownies'', as well as in instruction manuals for products like their ''1 & 1A Pocket "Kodaks" Juniors''. "Brief time" was also used in reference works like ''Newnes Photographers' Pocket Reference Book'' (1955).</ref><!--

 --> The instruction sheet further suggested an aperture of {{f/|11}} for Sashalite's larger flashbulb and {{f/|8}} for the smaller. However, apparently assuming photographers using their product would be doing so in a relatively narrow range of distances common to portraiture, made no mention of flash-to-subject distance. The instruction sheet then directed the photographer as follows:

<span style="font-style:roman;font-family:Georgia,serif>{{quote|Then simply:<br />1. Open the camera shutter.<br />2. Flash the "Sashalite" bulb.<br />3. Close the camera shutter.}}</span>

In 1932, [[Philips]] introduced what was arguably the first modern flashbulb with wire fill under the trade name "Hydronalium". Philips' technology was licensed in 1937 by Wabash Photolamp Corporation and introduced to the U.S. market as Superflash bulbs. Shortly later, in 1939, General Electric under their MAZDA brand introduced their very successful, golf ball-size, wire-filled, bayonet-base, Midget {{nowrap|No.&thinsp;5.}}<ref group=note>Known variously as ''G⋅E MAZDA Synchro-Press 5'', ''G⋅E MAZDA Mighty Midget Photoflash Lamp No. 5'', and after WWII, ''General Electric Sure•Fire Number 5.''</ref>

Prior to GE's ''inverse of the squares'' innovation, photographers and publications—via tedious trial and error with different flashbulbs and reflectors—generated tables providing a large number of aperture-distance combinations. For instance, a 1940 edition (written too late to incorporate guide numbers) of the ''Complete Introduction to Photography'' by the Journal of the Photographic Society of America featured an exposure table for foil-filled flashbulbs, which is shown below. The parenthetical values in bold were not part of the original table; they show the equivalent guide number for each aperture-distance combination.<!--

 --><ref group=note>The original table used the common nomenclature values for the apertures; the guide numbers shown here are based on the precise aperture values from the <math display="inline">{\sqrt{2}}^{\ n}</math> series.</ref><!--

 -->  Note the scatter in the guide number values in each column; the data for the right-most flashbulb setup has over a three-quarter f{{nbhyph}}stop variation from high to low.

{| border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f5f5f0; border: 2px #3E3E3E solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="6" style="background:#3E3E3E; text-align:center"|<span style="color:white;">1940 EXPOSURE EXPERIMENT WITH<br />FOIL-FILLED FLASHBULBS<br />''Complete Introduction to Photography'', p. 317</span>
|-
|style="text-align:center"|'''Distance<br />(in feet)'''
|style="text-align:center"|'''Small bulb<br />in metal<br />reflector'''
|style="text-align:center"|'''Large bulb<br />in metal<br />reflector'''
|style="text-align:center"|'''Small bulb<br />in ordinary<br />reflector'''
|style="text-align:center"|'''Large bulb<br />in ordinary<br />reflector'''
|-
|style="text-align:center"|6
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:22 '''(136)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:32 '''(192)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:16 '''(96)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:22 '''(136)'''
|-
|style="text-align:center"|10
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:16 '''(160)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:22 '''(226)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:11 '''(113)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:16 '''(160)'''
|-
|style="text-align:center"|15
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:11 '''(170)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:16 '''(240)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:6.3 '''(95)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:11 '''(170)'''
|-
|style="text-align:center"|20
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:6.3 '''(127)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:11 '''(226)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:4.5 '''(90)'''
|style="text-align:center"|<span style="font-style:italic;font-family:Georgia,serif>''f''</span>:6.3 '''(127)'''
|}

Bear in mind that the above table is ''for only one film speed''. For end users, obtaining proper exposures with flashbulbs was an error-prone effort as they mentally interpolated between distances and f{{nbhyph}}stop combinations that weren't very accurate in the first place. Had the guide number system existed by this point, the above table would not have required the left-most column showing distances and would have required only one row (showing guide numbers) under each heading.

By 1941, two years after GE introduced the guide number system, guide number ratings for products like the GE {{nowrap|No.&thinsp;11}} were being discussed  in books like ''Flash in Modern Photography.''<ref>{{cite book|last1=Mortensen|first1=William|title=Flash in Modern Photography|url=https://archive.org/details/flashinmodernpho00mort|date=1941|publisher=Camera Craft Publishing Co.|page=[https://archive.org/details/flashinmodernpho00mort/page/47 47]}}</ref> By 1944, the 16th edition of ''Wall's Dictionary of Photography'' featured a guide number table.<ref>{{cite book |editor-last1=Mortimer |editor-first1=F. J. |title=Wall's Dictionary of Photography |date=1944 |publisher=American Publishing Co |location=Boston |edition=16th |pages=313–314}} Revised and largely re-written by Sowerby, A. L. M.</ref> Perhaps so as to not intimidate readers, that table still showed numerous combinations of distances and apertures, but it also featured a new column showing the guide number that every cell in its row equalled. The guide number system underlying that table drove slightly finer increases, averaging a factor of <math>\sqrt{2}</math> each, from one distance to the next (6, 9, 12, 18, and 24 feet) so each step would be accompanied—by definition—by an increase in aperture of precisely one f{{nbhyph}}stop. Not surprisingly, the data scatter was as tight as mathematical rounding to the nearest foot permitted.

By late 1949, authors catering to hobbyists were using guide numbers in articles in a routine fashion, as exemplified by the January 1950 issue of ''Popular Photography'', as follows:&thinsp;<ref>Page 127</ref>

<span style="font-style:roman;font-family:Georgia,serif>{{quote|The system I use is to decide upon lens opening (as demanded by depth of field) and, working with the guide number of the bulb, figure out how far the flash should be from the subject.}}</span>

Upon introducing the new ''inverse of the squares'' concept in 1939, General Electric initially referred to the new system as "Flash Numbers".<ref name="Minicam" /> Two years later, ''Flash in Modern Photography'' (1941) used the term "guide number" on page 47, on the very next page used the term "Flash Number" (title case), and later still used the term "flash number" (lowercase). Terminology was similarly mixed in the United Kingdom for years after the introduction of the guide number system; circa 1954, "Flash Factor", "Flash number" (and sometimes "Guide number") were in use.<ref>{{cite book|last1=Newnes|first1=George|title=Newnes Photographers' Pocket Reference Book|date=1955|publisher=Butler & Tanner Ltd., Frome and London|page=84}}</ref>

== Glossary ==
{{glossary}}
{{term |1=[[Luminous flux]] (or luminous power)}}
{{defn |'''Symbol:''' ''Φ''<sub>v</sub> (pronounced ''[[Phi]] sub vee'')}}
{{defn |'''Unit:''' [[Lumen (unit)|Lumen]]}}
{{defn |'''Definition:''' In the context of flash devices, is the measure of the power of [[Luminosity function|eye-adjusted visible light]] being emitted. In common vernacular, it is the ''rate'' at which a flash device emits light during a flash.}}
{{term |1=[[Luminous energy]]}}
{{defn |'''Symbol:''' ''Q''<sub>v</sub>}}
{{defn |'''Unit:''' [[Lumen second|Lumen⋅second]]}}
{{defn |'''Definition:''' In the context of flash devices, is the measure of the total energy, or ''quantity'', of eye-adjusted visible light emitted over a period of time. In common vernacular, it is the total ''amount'' of light released over the course of a flash.}}
{{term |1=[[Illuminance]]}}
{{defn |'''Symbol:''' ''E''<sub>v</sub>}}
{{defn |'''Unit:''' [[Lux]] (lumens per square meter)}}
{{defn |'''Definition:''' In the context of photography, is the measure of the intensity, or concentration per unit area, of eye-adjusted visible light impinging upon a surface. In common vernacular, it is the ''brightness'' of light measured at the surface of a photographic subject.}}
{{term |1=[[Exposure (photography)|Luminous exposure]]}}
{{defn |'''Symbol:''' ''H''<sub>v</sub>}}
{{defn |'''Unit:''' Lux⋅second}}
{{defn |'''Definition:''' In the context of photography, is the measure of the total energy, or quantity, of eye-adjusted visible light that impinged upon a unit area over a specified period of time. In common vernacular, it is the product the ''brightness'' of light measured at the surface of a photographic subject times the ''duration'' of that light.}}
{{glossary end}}

== See also ==
* [[Exposure (photography)]]
* [[Exposure value]]
* [[Flash comparison]]
* [[Flash (photography)]]
* [[Flash synchronization]]
* [[Flashtube]]

== Notes ==
{{reflist|group=note|200em}}

== References ==
{{reflist|200em}}

== Further reading ==
* Bryan Peterson, ''Understanding Flash Photography: How to Shoot Great Photographs Using Electronic Flash'', (paperback – August 30, 2011), Amphoto Books, {{ISBN|9780817439569}}

== External links ==
* [http://www.sevenels.net/ D. 'n' A. Seaver:] ''[http://conleycameras.sevenels.net/ Conley cameras]''
* [https://www.photomemorabilia.co.uk/ Photographic Memorabilia:] [https://www.photomemorabilia.co.uk/Ilford/Flash_History.html ''Flash Photography ~ History & ILFORD'']
* [http://www.scantips.com/ Scantips.com:] [http://www.scantips.com/lights/flashbasics1c.html ''Understanding Flash Guide Numbers, plus guide number Calculator'']
* [http://www.scantips.com/ Scantips.com:] [http://www.scantips.com/lights/evchart.html ''EV – Exposure Value (with EV table and EV calculator)'']
* [http://www.sekonic.com/united-states/ Sekonic.com:] [http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx ''EV/Lux/FootCandle Conversion Chart''] {{Webarchive|url=https://web.archive.org/web/20170814220607/http://www.sekonic.com/united-states/support/evluxfootcandleconversionchart.aspx |date=2017-08-14 }}

{{Photography}}

[[Category:Flash photography]]
[[Category:Photographic lighting]]
[[Category:Light sources]]