0 gauge

American Wire Gauge Conversion Chart (AWG)

American Wire Gauge Conversion Chart (AWG)

American wire gauges (AWG) are a standard set of sizes for wire conductors — the smaller the wire gauge, the larger the diameter in inches or millimeters, and vice versa. Refer to this American wire gauge conversion chart to help determine the correct wire size to order.

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Gauge No. Inches Millimeters
10.289297 7.348

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O scale

O scale

Australian O scale model railway

Scale7 mm to 1 ft;
6.35 mm (0.25 inches) to 1 ft
Scale ratiovarious: 1:48 to 1:43.5
Model gauge30 mm (1.181 in) – 33 mm (1.3 in)
Prototype gauge1,435 mm (4 ft 8+1⁄2 in) standard gauge

O scale (or O gauge) is a scale commonly used for toy trains and rail transport modelling. Introduced by German toy manufacturer Märklin around 1900, by the 1930s three-railalternating current O gauge was the most common model railroad scale in the United States and remained so until the early 1960s. In Europe, its popularity declined before World War II due to the introduction of smaller scales.

O gauge had its heyday when model railroads were considered toys, with more emphasis placed on cost, durability, and the ability to be easily handled and operated by pre-adult hands. Detail and realism were secondary concerns, at best. It still remains a popular choice for those hobbyists who enjoy running trains more than they enjoy other aspects of modeling, but developments in recent years have addressed the concerns of scale model railroaders making O scale popular among fine-scale modellers who value the detail that can be achieved.

The size of O is larger than OO/HO layouts, and thus is a factor in making the decision to build an O gauge layout.

Collecting vintage O gauge trains is also popular and there is a market for both reproduction and vintage models.


The name for O gauge and O scale is derived from "0 [zero] gauge" or "Gauge 0" being smaller than Gauge 1 and the other then-existing standards. It was created in part because manufacturers realized their best selling trains were those built in the smaller scales.

In the United States, manufacturers such as the Ives Manufacturing Company, American Flyer, and Lionel Corporation used O gauge for their budget line, marketing either Gauge 1 or 'Wide gauge' (also known as 'standard gauge') as their premium trains. One of the Lionel Corporation's most popular trains, the 203 Armoured Locomotive, was O gauge and ran on tracks with rails spaced 1.25 inches apart. The Great Depression wiped out demand for the expensive larger trains, and by 1932, O gauge was the standard, almost by default.

Because of the emphasis on play value, the scale of pre-World War II O gauge trains varied. The Märklin specifications called for 1:43.5 scale. However, many designs were 1:48 scale or 1:64 scale. Early Marx Trains and entry-level trains, usually made of lithographed tin plate, were not scaled at all, made to whimsical proportions about the same length of an HO scale ("half O") piece, but about the same width and height of an O scale piece. Yet all of these designs ran on the same track, and, depending on the manufacturer(s) of the cars, could sometimes be coupled together and run as part of the same train.

After World War II, manufacturers started paying more attention to scale, and post-war locomotives and rolling stock tended to be larger and more realistic than their earlier counterparts. This has been reflected in the change of name from O gauge to O scale: gauge describes merely the distance between the rails, while scale describes the size ratio of a model as it relates to its real-world prototype.

Since the early 1990s, O scale manufacturers have begun placing more emphasis on realism, and the scale has experienced a resurgence in popularity, although it remains less popular than HO or N scale. However, newer manufacturers including MTH Electric Trains, Lionel, LLC, Atlas Model Railroad Co and Weavermodels[1] are making very exact, 1:48 scale models of trains.

In the United Kingdom the dominant O gauge manufacturer before World War II was Meccano Ltd. who from 1920 produced a range of clockwork and electric models under the "Hornby" name.


The differences in the various O gauge and O scale standards can be confusing. O gauge model railroad tracks typically have their rails spaced 1.25 in (31.75 mm) apart[2] with the United States National Model Railroad Association (NMRA) standard allowing spacings between 31.75 mm and 32.64 mm.[3]

Scale and gauge[edit]

Scale refers to the size of the model relative to the actual full-sized object being represented, while gauge is the width of the model track. Most commercially produced model track is a compromise between appearance and a trouble-free running surface.


Scale is the ratio of a model dimension to the real life dimension. O Scale in the UK is commonly 1:43.5 or 7 mm to the foot, in continental Europe it is commonly 1:45 though 1:43.5 is also used particularly in France,[4] and in the USA 1:48.[3] Each region tends to design models to its own scale.[citation needed] The NMRA and the MOROP maintain detailed standards for a variety of scales to help model makers create interoperable models.[4][5]


Gauge refers to the distance between the inside edges of the load-bearing rails. Various sizes of track gauge exist around the world and the normal O gauge track represents the Standard gauge of 1,435 mm (4 ft 8+1⁄2 in). "O gauge" refers to tracks that are 1.25 in (31.75 mm) apart.[2] When used as a narrow-gauge track, O gauge allows scales such as 1:32 representing 1,000 mm (3 ft 3+3⁄8 in) gauge track. 1:20 representing 600 mm (1 ft 11+5⁄8 in) narrow-gauge railways.

Regional model manufacturers design their O-scale rolling stock with minor regional scale differences — manufacturers support their rolling stock with track made to the same regional scales, so there is no universal width for O-gauge model track.[citation needed] Models could represent the real-world standard gauge track spacing of 1,435 mm by choosing various spacings such as 30 mm (1.181 in) at 1:48 scale, 1.25 in (31.75 mm) at 1:45.2 scale, 32 mm (1.26 in) at 1:44.8 scale, 32.96 mm (1.298 in) at 7 mm:1 ft scale, and 33 mm (1.3 in) at 1:43.5 scale. Model makers choose their scale based on many considerations including the existing marketplace, aesthetic concerns and compatibility with existing models.

Wide- or narrow-gauge track[edit]

Probably the oldest known 0e gauge vehicles in the MCB from 1947. WAB rack railway train, 2021

Some O-scale modelers choose to model prototypes at other than standard gauge and follow wide gauge (also known as broad-gauge) or narrow-gauge railroads. There is no standard for wide- or narrow-gauge model track, and modelers wishing to portray such railway track either build their own, or more commonly accept the shortcomings of appropriately wider or narrower gauge model track. 16.5 mm (0.65 in), 12 mm (0.472 in) and 9 mm (0.354 in) are the more popular track widths used by indoor enthusiasts modeling narrow gauge. Differences in regional scales give different prototype gauges to these different model track widths.

For example, using specially manufactured 16.5 mm (0.65 in) gauge track, scaled at 7 mm to the foot (with appropriately spaced, larger sleepers, etc.) underneath:

  1. UK O scale rolling stock (1:43.5), it becomes a narrow-gauge track of 2 ft 4 in (711 mm), and is referred to as "On 16.5" [modelers portray gauges between 2 ft (610 mm) and 3 ft (914 mm)].
  2. European O scale rolling stock (1:45 or 1:43.5 in France), it becomes a narrow-gauge track of 750 mm (2 ft 5+1⁄2 in), and is referred to as "Oe" portraying a 750 mm prototype.
  3. United States O scale rolling stock (1:48), it becomes a narrow-gauge track of 2 ft 6 in (762 mm), and is referred to as "On 2½" (or On30, as in 30 inches).

O-27 gauge[edit]

O-27 gauge is a United States variant whose origins are slightly unclear. Some historians attribute its creation to A. C. Gilbert Company's American Flyer, but Ives Manufacturing Company used O-27 track in its entry-level sets at least a decade before Gilbert bought Flyer.

The modern standard for O-27, however, was formalized after 1938 by Gilbert, who scaled the locomotives and rolling stock to 1:64 scale. After World War II, this practice was continued by Louis Marx and Company, who used it throughout its product line, and Lionel, who used it for its entry-level trains. O-27 track is spaced at the same width as regular O gauge track, but is slightly shorter in height and has thinner rails than traditional O gauge track. A shim underneath the O-27 track enables the use of O and O-27 track together.

The O-27 name comes from the size of the track's curves. A circle made of eight pieces of standard 45-degree curved O gauge track will have a 31 inches (787 mm) diameter. A circle made of 8 pieces of 45-degree curved O-27 track is smaller, with a 27 inches (686 mm) diameter. Full-sized O cars sometimes have difficulty negotiating the tighter curves of an O-27 layout.

Although the smaller, tin lithographed cars by American Flyer, Marx, and others predate the formal O-27 standard, they are also often called O-27, because they also operate flawlessly on O-27 track. Marx may have dedicated its entire line to 0-27, but the Lionel Corporation remains to produce O-27 track and trains. Its tubular rail is a standard of the tinplate era.

Super-O gauge[edit]

"Super-O gauge" is a variant whose origin stems from Lionel's desire to create a more realistic looking track and improve sagging sales in the late 1950s.

Exact scale standards[edit]

Dissatisfaction with these standards led to a more accurate standard for wheels and track called Proto:48 This duplicates to exact scale the AAR track and wheel standards.[6] In the United Kingdom a similar ScaleSeven system exists.

The track gauge normally used for 0 of 32 mm or the near-approximation 1+1⁄4 inch is for Standard gauge (1,435 mm (4 ft 8+1⁄2 in)) approximately equivalent to 5 ft (1,524 mm) at 1:48 scale, 4 ft 8+1⁄2 in (1,435 mm) at 1:45 and 4 ft 6+1⁄2 in (1,384 mm) at 1:43.5.[7]

Possibly because of the large size of American railroad systems, accurate scale modeling in standard gauge O gauge is rare in the United States, though narrow-gauge modeling is much more common.

Four common narrow-gauge standards exist, and the differences among On3,On2,On30, and On18 are frequent sources of confusion. On3 is exact-scale 1:48 modeling of 3 ft (914 mm) gauge prototypes, while On30 is 1:48 modeling of 2 ft 6 in (762 mm) gauge prototypes, On2 is 1:48 modeling of 2 ft (610 mm) gauge prototypes, and On18 is 1:48 modeling of 18 in (457 mm) gauge prototypes. On30 is also sometimes called On2½.

Because On30's gauge closely matches that of HO track, On30 equipment typically runs on standard HO scale track. While many On30 modelers scratchbuild their equipment, commercial offerings in On30 are fairly common and sometimes very inexpensive, with Bachmann Industries being the most commonly found manufacturer.

Hobbyists who choose to model in any of these O gauge standards nevertheless end up building most, if not all, of their equipment either from kits or from scratch.

Power supply[edit]

Models that are either built to 1:43 scale, 7 mm:1 foot (1:43.5), 1:45 scale, or 1:48 scale can run on realistic-looking two-rail track using direct current (Commonly known as 2-Rail O), or on a center third power rail or a center stud supply system. If modeling such a system, an external third rail or overhead supply may be employed.

While two-rail O has traditionally been more popular in Europe, and alternating current powered three-rail more popular in the United States, two-rail O is currently experiencing a resurgence in popularity in the United States, due to increased availability of ready-to-run models from several manufacturers. The recent development of Digital Command Control (DCC) power systems with built in sound have also increased the popularity of two rail O scale models.

Die-cast metal models compatible with O scale[edit]

Many manufacturers produce die-cast models of trucks, cars, buses, construction equipment and other vehicles in scales compatible with or similar to O scale model trains. These are available in 1:43 scale, 1:48 scale and 1:50 scale. Manufacturers include Conrad, NZG, Corgi, TWH Collectibles. Ertl, and many others. These are popular with collectors and easy to find.

Geographical area[edit]

A 242A1 locomotive and standard gauge track at some model railway scales

European (other than UK and former USSR)[edit]

0 scale is one of the scales defined by the NEM as 1:45 scale. However, for historical reasons they use the number "zero" rather than the letter as the name for the scale.

A situation similar to that in Britain exists in continental Europe, although the market revolves less around kits and more around expensive hand-built metal models for the deep-pocketed collector. Additionally, Czech Republic-based Electric Train Systems started manufacturing and selling lithographed tin 1:45 scale trains in 1991, citing O gauge's advantages over smaller sizes for non-permanent floor layouts and outdoor layouts. The Spanish company Paya produces a smaller line of tinplate trains, based on designs dating back to 1906.

In Germany a narrow-gauge train set is produced by Fleischmann, running on 16.5 mm (0.65 in) track, this scale is called "0e" (750 mm (2 ft 5+1⁄2 in) prototype). The trains are marketed as children's toy trains (Magic Train), but are accurately built after Austrian prototypes and increased the interest in building narrow-gauge layouts in Germany and Austria significantly. Since 2006 there are again some reasonably priced O-scale plastic models available, manufactured by DCC developer Lenz.

In the 1970s both Italian branches of Rivarossi and Lima produced large quantities of "0" models, mainly Italian and German trains, later on coaches and wagons from Switzerland. In the late 1970s hand made models of the Orient Express could be found in several German hobby stores, along with other highly detailed accessories. Special brands for high procession were Lemaco, Fulgurex, Euro Train, Markscheffel & Lennartz, making models in small quantities.

Former Soviet Union[edit]

Between 1951 and 1969, a limited number of O gauge train sets were manufactured in the Soviet Union. Utilizing the same track and voltage as their U.S. counterparts, the colorful locomotives and cars resembled pre-World War II designs from U.S. manufacturers Lionel and American Flyer and the couplers were nearly identical to those of pre-war American Flyer. Some differences in U.S. and Soviet railroading were evident from comparing the Soviet sets with U.S. sets, particularly in the design of the boxcar, which looked like an American Flyer boxcar with windows added, reflecting the Soviets' use of box cars to haul livestock, as well as merchandise.

Much like their U.S. counterparts, Soviet O gauge trains were toys, rather than precision-scaled models.


United Kingdom[edit]

In the United Kingdom, O gauge equipment is produced at a scale of 1:43.5, which is 7 mm to the foot (using the common British practice of modelling in metric prototypes originally produced using Imperial measurements). It is often called 7 mm scale for this reason.

Although toy trains were historically produced to this scale, O gauge's popularity across the whole of Europe reduced after World War II, and the standard is rarer than in the United States. Modelling in O gauge in fact almost died out in Britain but enjoyed a resurgence in the 1990s as modellers developed a new appreciation for the level of accurate detailing possible in this scale. Some ready to run models are produced in this scale but most are available only as kits for assembly by the modeller or a professional model-builder. O gauge is considered an expensive scale to model in although the necessarily smaller scope of a larger-scaled layout mitigates this to some extent. The two dominant British manufacturers, Bassett-Lowke and Hornby, ceased production of O gauge trains in 1965 and 1969, respectively. However, ACE Trains and for a while a revived Bassett-Lowke are once again producing tinplate O gauge sets, many of them reproductions of classic Hornby and Bassett-Lowke designs, and Heljan also recently joined the market producing O gauge Diesel locomotives.

A true-to-prototype version of British 7 mm O gauge exists, called ScaleSeven (S7) which uses 33 mm gauge to represent British standard gauge in a scale of 1:43.5.

The British 1:43.5 rail scale gave birth to series of die cast cars and model commercial vehicles of the same scale which gradually grew in popularity and spread to France, the rest of Europe and North America at the same time that the rail models were becoming less popular.

7 mm scale is also popular for modelling narrow-gauge railways, a section of the hobby supported by the 7mm Narrow Gauge Association.

United States[edit]

In the United States, O gauge is defined as 1:48 (0.25 inches to the foot, "quarter inch scale" 1/4 inch equals one foot). This is also a common dollhouse scale, giving more options for buildings, figures, and accessories. Many O gauge layouts are also accessorized with 1:43.5 scale model cars.

While 1:48 is a very convenient scale for modeling using the Imperial system (a quarter-inch equals one scale foot), the discrepancy between O gauge in the United States and O gauge in Europe is attributed to Lionel misreading the original Märklin specifications.

Although Lionel is the most enduring brand of O gauge trains, a variety of manufacturers made trains in this scale. Prior to World War I, the majority of toy trains sold in the United States were German imports made by Märklin, Bing, Fandor, and other companies. World War I brought a halt to these German imports, and protective tariffs after the war made it difficult for them to compete.

In between the two world wars, shorter-lived companies such as Dorfan, Hafner, Ives, and Joy Line competed with Lionel, Louis Marx and Company, American Flyer and Hornby. Many of these pre-war trains operated by clockwork or battery power and were made of lithographed tin. The sizes of the cars varied widely, as the standard for O gauge was largely ignored. Dorfan went out of business in 1934, while Ives was bought by Lionel, and Hafner and Joy Line were bought by Marx. Hornby withdrew from the U.S. market in 1930 after selling its U.S. factory to the A. C. Gilbert Company.

As early as 1938, the survivors Lionel, Marx, and American Flyer faced competition from Sakai, a Tokyo-based Japanese toy company who sold trains priced at the low end of the market. The product designs most closely resembled Lionel, but with Märklin-like couplers and detail parts that appeared to be copied from Ives. "Seki", another Japanese company, was an entirely different and independent company.

Between 1946 and 1976, the primary U.S. manufacturers of O gauge trains were Lionel and Marx, with American Flyer switching to the more-realistic S scale and the rest of the companies out of business.

Toy maker Unique Art produced a line of inexpensive O gauge trains from 1949 to 1951, but found itself unable to compete with Marx. Marx continued to make clockwork and battery-powered trains and lithographed cars into the 1970s, along with more realistic offerings that were sometimes difficult to distinguish from Lionel.

Sakai re-entered the U.S. market after World War II, selling trains that were often nearly identical to Marx designs and sometimes undercutting Marx's prices, from 1946 to 1969.

A company called American Model Toys brought out a line of realistic, detailed cars beginning in 1948. In 1953 it released a budget line. It ran into financial difficulty, reorganized under the name Auburn Model Trains, and ended up selling its line to Nashville, Tennessee-based Kusan, a plastics company who continued its production until 1961. The tooling was then sold to a small company run by Andrew (Andy) Kriswalus in Endicott, New York, who operated as Kris Model Trains, or KMT. Andy Kriswalus only produced the box, stock, and refrigerator cars from the Kusan dies, and on some of these cars he mounted die-cast trucks from the Kusan tooling. After Kriswalus' death, the tooling was sold to K-Line and Williams Electric Trains, who continued to use it to produce parts of their budget lines.

From O gauge's beginnings up until the mid-1970s, the various manufacturers' trackside accessories would interoperate with one another, but the train cars themselves used couplers of differing designs, often making it difficult or impossible to use different manufacturers' cars together. The post-War consolidation did little to improve matters: Marx used three different standards, depending on the product line, and Lionel used two, so frequently the companies' own entry-level products were incompatible with their high-end products, let alone with the competition. Hobbyists who wanted differing standards to interoperate had to resort to replacing couplers.

After Marx went out of business in 1978, K-Line bought much of Marx's tooling and entered the marketplace. K-Line's early offerings changed little from the old Marx designs, other than a new brand name and a Lionel-compatible coupler, making K-Line's offerings completely interoperable with Lionel.

As O gauge regained popularity in the 1990s it also started to regain manufacturers, and as of late 2003, no fewer than six companies market O gauge locomotives and/or cars, all theoretically interoperable with one another.

Lionel equipment retains a large collector following. Equipment from shorter-lived manufacturers prior to World War II is also highly sought after, while American Flyer and Marx are less so. Post-War Marx is gaining in popularity after years of being derided by serious collectors. There is little collector interest in Sakai today, possibly because of difficulty identifying the equipment and because the brand is much less widely known than its U.S. counterparts.

In the recent years there has been a movement called 3-Rail Scale. It is three-rail trains on high-rail track, but with scale couplers and other more prototypical details, like fixed pilots and scale wheels. Most 3-Rail scale modelers use Kadee brand scale couplers.

The biggest makers of American O scale trains today are Lionel, LLC, MTH Electric Trains, Atlas O, and Weaver Models.

In popular culture[edit]

This scale and gauge was used to model the Skarloey Railway locomotives and rolling stock for series 4 of Thomas the Tank Engine & Friends. However, the construction of the engines resulted in difficulties during filming. Series 5 introduced new models of the engines and rolling stock, which were bigger than the gauge 1 standard gauge engines and stock but still ran on O gauge track. They were used up until series 12 before the move to CGI animation. The small scale models occasionally still appeared, usually when interacting with gauge 1 standard gauge engines in series 5, 7 (stock footage), 9 and 10 and Calling All Engines!.

See also[edit]


External links[edit]

Wikimedia Commons has media related to O scale.
Sours: https://en.wikipedia.org/wiki/O_scale
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American wire gauge

North American standard for electrical wire diameters

"AWG" redirects here. For other uses, see AWG (disambiguation).

American Wire Gauge (AWG), also known as the Brown & Sharpe wire gauge, is a logarithmicsteppedstandardizedwire gauge system used since 1857, predominantly in North America, for the diameters of round, solid, nonferrous, electrically conducting wire. Dimensions of the wires are given in ASTM standard B 258.[1] The cross-sectional area of each gauge is an important factor for determining its current-carrying ampacity.

Increasing gauge numbers denote decreasing wire diameters, which is similar to many other non-metric gauging systems such as British Standard Wire Gauge (SWG), but unlike IEC 60228, the metric wire-size standard used in most parts of the world. This gauge system originated in the number of drawing operations used to produce a given gauge of wire. Very fine wire (for example, 30 gauge) required more passes through the drawing dies than 0 gauge wire did. Manufacturers of wire formerly had proprietary wire gauge systems; the development of standardized wire gauges rationalized selection of wire for a particular purpose.

The AWG tables are for a single, solid and round conductor. The AWG of a stranded wire is determined by the cross-sectional area of the equivalent solid conductor. Because there are also small gaps between the strands, a stranded wire will always have a slightly larger overall diameter than a solid wire with the same AWG.

AWG is also commonly used to specify body piercing jewelry sizes (especially smaller sizes), even when the material is not metallic.[2]


By definition, Nr. 36 AWG is 0.005 inches in diameter, and Nr. 0000 is 0.46 inches in diameter, or nearly half-an-inch. The ratio of these diameters is 1:92, and there are 40 gauge sizes from the smallest Nr. 36 AWG to the largest Nr. 0000{ {sc }}, or 39 steps. Because each successive gauge number increases cross sectional area by a constant multiple, diameters increase geometrically with falling gauge number. Any two successive gauges (e.g., A and B ) have diameters whose ratio (dia. B ÷ dia. A) is {\displaystyle {\sqrt[{39}]{92}}\approx 1.12293\;,} while for gauges two steps apart (e.g., A, B, and C), the ratio of the C to A is about (1.12293)² ≈ 1.26098 .

The diameter of an AWG wire is determined according to the following formula:

{\displaystyle d_{n}=0.005\;{\text{inch}}\times 92^{(36-n)/39}=0.127\;{\text{mm}}\times 92^{(36-n)/39}~.}

(where n is the AWG size for gauges from 36 to 0, n = −1 for Nr. 00, n = −2 for AWG 000, and n = −3 for AWG 0000. See rule below.)

or equivalently:

{\displaystyle {\begin{aligned}d_{n}&=~e^{(-1.12436-0.11594n)}\,{\text{inch}}&&=~e^{(2.1104-0.11594n)}\,{\text{mm}}\\&=~\left(0.324860{\text{ inches }}\right)\,\left(0.8905287\right)^{n}~&&=~\left(8.25154{\text{ mm }}\right)\,\left(0.8905287\right)^{n}~.\end{aligned}}}[b]

The gauge number can be calculated from the diameter using the following formulas:[c]

Step 1
Calculate the ratio{\displaystyle \,{\mathcal {R}}\,} of the wire's diameter {\displaystyle \,d\,} to the standard gauge (AWG #36 )
{\displaystyle {\mathcal {R}}={\frac {\;d_{\text{ [inch] }}\;}{0.005\,{\text{ inch }}}}={\frac {d_{\text{ [mm] }}}{\;0.127\,{\text{ mm }}\;}}}
where the middle expression with {\displaystyle \,d_{\text{[inch]}}\,} is used if {\displaystyle \,d\,} is measured in inches, and the right-hand expression with {\displaystyle \,d_{\mathrm {[mm]} }\,} when {\displaystyle \,d\,} is measured in millimeters.[d]
Step 2
Calculate the American wire gauge numbern using any convenient logarithm; pick any one of the following expressions in the last two columns of formulas to calculate n; notice that they differ in the choice of base of the logarithm, but otherwise are identical:
{\displaystyle {\begin{aligned}n=\;-39\log _{92}({\mathcal {R}})+36\;&=\;-39{\frac {\log _{10}({\mathcal {R}})}{\;\log _{10}(92)\;}}\,+36\;&&=\;-39{\frac {\ln({\mathcal {R}})}{\;\ln(92)\;}}\;\;\,+36\;\\\\&=\;-39{\frac {\log _{e}({\mathcal {R}})}{\;\log _{e}(92)\;}}\;+36\;&&=\;-39{\frac {\log _{2}({\mathcal {R}})}{\;\log _{2}(92)\;}}+36\;\\\\&=\;-39{\frac {\ log_{B}({\mathcal {R}})}{\;\log _{B}(92)\;}}+36~,\\\end{aligned}}}
In general, the calculation can be done using any base B strictly greater than zero.[e]

and the cross-section area is

{\displaystyle A_{n}={\frac {\pi }{4}}d_{n}^{2}\approx \left(\,0.000019635{\text{ inch }}\,\right)^{2}\times 92^{(36-n)/19.5}\approx \left(\,0.012668{\text{ mm }}\,\right)^{2}\times 92^{(36-n)/19.5}\;.}

The standard ASTM B258-02 defines the ratio between successive sizes to be the 39th root of 92, or approximately 1.1229322.[3] ASTM B258-02 also dictates that wire diameters should be tabulated with no more than 4 significant figures, with a resolution of no more than 0.0001 inches (0.1 mils) for wires larger than Nr. 44 AWG, and 0.00001 inches (0.01 mils) for wires Nr. 45 AWG and smaller.

Very fat wires have gauge` sizes denoted by multiple zeros – 0, 00, 000, and 0000 – the more zeros, the larger the wire, starting with AWG 0. The two notations overlap when the 2 step formula for n , above, produces zero. In that case the gauge number n is zero, it's taken as-is. If n is a negative number, the gauge number is notated by multiple zeros, up to just under a half-inch; beyond that point, the “wire” may instead considered a copper bar or rod. The gauge can be denoted either using the long form with several zeros or the short form z "/0" called gauge "number of zeros/0" notation. For example 4/0 is short for AWG 0000. For an z /0 AWGwire, use the number of zeros {\displaystyle \;z=-n+1~{\mathsf {\text{ for }}}~n<0\;,}   and similarly   {\displaystyle \;n=-z+1~{\mathsf {\text{ for }}}~z>0~.} in the above formulas. For instance, for AWG 0000 or 4/0, use {\displaystyle \,n=-4+1=-3~.}

Rules of thumb[edit]

The sixth power of 39√92 is very close to 2,[4] which leads to the following rules of thumb:

  • When the cross-sectional area of a wire is doubled, the AWG will decrease by 3 . (E.g. two AWG Nr. 14 wires have about the same cross-sectional area as a single AWG nr. 11 wire.) This doubles the conductance.
  • When the diameter of a wire is doubled, the AWG will decrease by 6 . (E.g. AWG nr. 2 is about twice the diameter of AWG nr. 8 .) This quadruples the cross-sectional area and the conductance.
  • A decrease of ten gauge numbers, for example from nr. 12 to nr. 2, multiplies the area and weight by approximately 10, and reduces the electrical resistance (and increases the conductance) by a factor of approximately 10.
  • For the same cross section, aluminum wire has a conductivity of approximately 61% of copper, so an aluminum wire has nearly the same resistance as a copper wire smaller by 2 AWG sizes, which has 62.9% of the area.
  • A solid round 18 AWG wire is about 1 mm in diameter.
  • An approximation for the resistance of copper wire may be expressed as follows:
mΩ/ftmΩ/m AWG
mΩ/ftmΩ/m AWG
mΩ/ftmΩ/m AWG
000  0.0640.2 8  0.64  2 18  6.4  20 28  64200
00  0.080.25 9  0.82.5 19  8  25 29  80250
0  0.10.32 10  13.2 20  10  32 30  100320
1  0.1250.4 11  1.25 4 21  12.5 40 31  125400
2  0.160.5 12  1.65 22  16  50 32  160500
3  0.20.64   13  26.4 23  20  64 33  200640
4  0.250.8 14  2.5  8 24  25  80 34  250800
5  0.321.0 15  3.2  10 25  32  100 35  3201,000
6  0.641.25   16  412.5 26  40  125 36  4001,250
7  0.51.6 17  516 27  50  160 37  5001,600

Tables of AWG wire sizes[edit]

The table below shows various data including both the resistance of the various wire gauges and the allowable current (ampacity) based on a copper conductor with plastic insulation. The diameter information in the table applies to solid wires. Stranded wires are calculated by calculating the equivalent cross sectionalcopperarea. Fusing current (melting wire) is estimated based on 25 °C (77 °F) ambient temperature. The table below assumes DC, or AC frequencies equal to or less than 60 Hz, and does not take skin effect into account. "Turns of wire per unit length" is the reciprocal of the conductor diameter; it is therefore an upper limit for wire wound in the form of a helix (see solenoid), based on uninsulated wire.

AWG Diameter Turns of wire,
Area Copper wire
Resistance per unit length[6]Ampacity at temperature rating[f]Fusing current[9][10]
60 °C 75 °C 90 °C Preece[11][12][13][14]Onderdonk[15][14]
(in) (mm) (per in) (per cm) (kcmil) (mm2) (mΩ/m[g]) (mΩ/ft[h]) (A) ~10 s 1 s 32 ms
0000 (4/0)0.4600[i]11.684[i]2.170.8562121070.16080.049011952302603.2 kA33 kA182 kA
000 (3/0)0.409610.4052.440.96116885.00.20280.061801652002252.7 kA26 kA144 kA
00 (2/0)0.36489.2662.741.0813367.40.25570.077931451751952.3 kA21 kA115 kA
0 (1/0)0.32498.2513.081.2110653.50.32240.098271251501701.9 kA16 kA91 kA
10.28937.3483.461.3683.742.40.40660.12391101301451.6 kA13 kA72 kA
20.25766.5443.881.5366.433.60.51270.1563951151301.3 kA10.2 kA57 kA
30.22945.8274.361.7252.626.70.64650.1970851001151.1 kA8.1 kA45 kA
40.20435.1894.891.9341.721.20.81520.2485708595946 A6.4 kA36 kA
50.18194.6215.502.1633.116.81.0280.3133795 A5.1 kA28 kA
60.16204.1156.172.4326.313.31.2960.3951556575668 A4.0 kA23 kA
70.14433.6656.932.7320.810.51.6340.4982561 A3.2 kA18 kA
80.12853.2647.783.0616.58.372.0610.6282405055472 A2.5 kA14 kA
90.11442.9068.743.4413.16.632.5990.7921396 A2.0 kA11 kA
100.10192.5889.813.8610.45.263.2770.9989303540333 A1.6 kA8.9 kA
110.09072.30511.04.348.234.174.1321.260280 A1.3 kA7.1 kA
120.08082.05312.44.876.533.315.2111.588202530235 A1.0 kA5.6 kA
130.07201.82813.95.475.182.626.5712.003198 A798 A4.5 kA
140.06411.62815. A633 A3.5 kA
150.05711.45017.56.903.261.6510.453.184140 A502 A2.8 kA
160.05081.29119.77.752.581.3113.174.01618117 A398 A2.2 kA
170.04531.15022.18.702.051.0416.615.06499 A316 A1.8 kA
180.04031.02424.89.771.620.82320.956.38510141683 A250 A1.4 kA
190.03590.91227.911.01.290.65326.428.05170 A198 A1.1 kA
200.03200.81231.312.31.020.51833.3110.1551158.5 A158 A882 A
210.02850.72335.113.80.8100.41042.0012.8049 A125 A700 A
220.02530.64439.515.50.6420.32652.9616.143741 A99 A551 A
230.02260.57344.317.40.5090.25866.7920.3635 A79 A440 A
240.02010.51149.719.60.4040.20584.2225.672.13.529 A62 A348 A
250.01790.45555.922.00.3200.162106.232.3724 A49 A276 A
260.01590.40562.724.70.2540.129133.940.811.32.220 A39 A218 A
270.01420.36170.427.70.2020.102168.951.4717 A31 A174 A
280.01260.32179.131.10.1600.0810212.964.900.831.414 A24 A137 A
290.01130.28688.835.00.1270.0642268.581.8412 A20 A110 A
300.01000.25599.739.30.1010.0509338.6103.20.520.8610 A15 A86 A
310.008930.22711244.10.07970.0404426.9130.19 A12 A69 A
320.007950.20212649.50.06320.0320538.3164.10.320.537 A10 A54 A
330.007080.18014155.60.05010.0254678.8206.96 A7.7 A43 A
340.006300.16015962.40.03980.0201856.0260.90.180.35 A6.1 A34 A
350.005610.14317870.10.03150.01601079329.04 A4.8 A27 A
360.00500[i]0.127[i]20078.70.02500.01271361414.84 A3.9 A22 A
370.004450.11322588.40.01980.01001716523.13 A3.1 A17 A
380.003970.10125299.30.01570.007972164659.63 A2.4 A14 A
390.003530.08972831110.01250.006322729831.82 A1.9 A11 A
400.003140.07993181250.009890.00501344110491 A1.5 A8.5 A
  1. ^ Note that, to the a little error in the last digits, {\displaystyle 8.25154{\text{ mm }}\approx \left(25.4{\text{ mm/inch }}\right)\times 0.324860{\text{ inches }}.}
  2. ^ The logarithm base 92 can be computed using any other logarithm, such as common or natural logarithm, using {\displaystyle \;\log _{92}(x)={\frac {\log _{B}x}{\log _{B}92}}~,} where B is any base for a logarithm – any number bigger than zero. Common values of “ B ” are 10 (base 10 logarithms, usually shown as just on the keys of most calculators; a more explicit notation is to write out {\displaystyle \,\log _{10}(\cdot )~}). Likewise, most hand calculators show the natural logarithm as , or more explicitly as {\displaystyle \,\log _{e}(\cdot )\equiv \ln(\cdot )~,} where e is Euler's number, {\displaystyle \,e\approx 2.7182819~.}Any logarithm will do, including exotic logarithms such as the binary or base-two logarithm {\displaystyle \;\log _{2}(\cdot )~;} the only caveat is that the same logarithm must be used throughout any one calculation.
  3. ^ Since {\displaystyle \,0.005\,{\text{[inch]}}=0.127\,{\text{mm}}\,,}exactly, by definition of the inch: {\displaystyle \;1\,{\text{ inch }}\equiv 25.4{\text{ mm }}\;} defines the value of the inch. The two expressions for the ratio {\displaystyle \,{\mathcal {R}}\,} always produce the same number (when the correct units of measure are used for {\displaystyle \,d\,} in each). Note that the units of {\displaystyle \;{\frac {\text{[inch]}}{\,{\text{[inch]}}\,}}\;} divide out, as do {\displaystyle \;{\frac {\text{[mm]}}{\,{\text{[mm]}}\,}}\;} producing a "pure number".
  4. ^ That is: You can use any logarithm you want, or have available, so long as the logarithm's base (B) is the same in both the numerator and denominator for any one calculation.
  5. ^For enclosed wire at 30 °C ambient,[7] with given insulation material temperature rating, or for single unbundled wires in equipment for 16 AWG and smaller.[8]
  6. ^or, equivalently, Ω/km
  7. ^or, equivalently, Ω/kft
  8. ^ abcdExactly, by definition

In the North American electrical industry, conductors larger than 4/0 AWG are generally identified by the area in thousands of circular mils (kcmil), where 1 kcmil = 0.5067 mm2. The next wire size larger than 4/0 has a cross section of 250 kcmil. A circular mil is the area of a wire one mil in diameter. One million circular mils is the area of a circle with 1,000 mil (1 inch) diameter. An older abbreviation for one thousand circular mils is MCM.

Stranded wire AWG sizes[edit]

AWG gauges are also used to describe stranded wire. The AWG gauge of a stranded wire represents the sum of the cross-sectional areas of the individual strands; the gaps between strands are not counted. When made with circular strands, these gaps occupy about 25% of the wire area, thus requiring the overall bundle diameter to be about 13% larger than a solid wire of equal gauge.

Stranded wires are specified with three numbers, the overall AWG size, the number of strands, and the AWG size of a strand. The number of strands and the AWG of a strand are separated by a slash. For example, a 22 AWG 7/30 stranded wire is a 22 AWG wire made from seven strands of 30 AWG wire.

As indicated in the Formulas and Rules of Thumb sections above, differences in AWG translate directly into ratios of diameter or area. This property can be employed to easily find the AWG of a stranded bundle by measuring the diameter and count of its strands. (This only applies to bundles with circular strands of identical size.) To find the AWG of 7-strand wire with equal strands, subtract 8.4 from the AWG of a strand. Similarly, for 19-strand subtract 12.7, and for 37 subtract 15.6. See the Mathcad worksheet illustration of this straightforward application of the formula.

Calculation of diameter and area in Mathcad

Measuring strand diameter is often easier and more accurate than attempting to measure bundle diameter and packing ratio. Such measurement can be done with a wire gauge go-no-go tool such as a Starrett 281 or Mitutoyo 950–202, or with a caliper or micrometer.

Nomenclature and abbreviations in electrical distribution[edit]

Main article: Electric power distribution

Alternative ways are commonly used in the electrical industry to specify wire sizes as AWG.

  • 4 AWG (proper)
    • #4 (the number sign is used as an abbreviation of "number")
    • № 4 (the numero sign is used as an abbreviation for "number")
    • No. 4 (an approximation of the numero is used as an abbreviation for "number")
    • No. 4 AWG
    • 4 ga. (abbreviation for "gauge")
  • 000 AWG (proper for large sizes)
    • 3/0 (common for large sizes) Pronounced "three-aught"
    • 3/0 AWG
    • #000


AWG is colloquially referred to as gauge and the zeros in large wire sizes are referred to as aught. Wire sized 1 AWG is referred to as "one gauge" or "No. 1" wire; similarly, smaller diameters are pronounced " gauge" or "No. " wire, where is the positive-integer AWG number. Consecutive AWG wire sizes larger than No. 1 wire are designated by the number of zeros:

  • No. 0, often written 1/0 and referred to as "one aught" wire
  • No. 00, often written 2/0 and referred to as "two aught" wire
  • No. 000, often written 3/0 and referred to as "three aught" wire

and so on.

See also[edit]


  1. ^"ASTM B258-14 Standard Specification for Standard Nominal Diameters and Cross-sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors". West Conshohocken: ASTM International. Archived from the original on 22 July 2014. Retrieved 22 March 2015.
  2. ^SteelNavel.com Body Piercing Jewelry Size Reference — illustrating the different ways that size is measured on different kinds of jewelry
  3. ^Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors (Report). 2008. p. 4. ASTM B258-02.[full citation needed]
  4. ^The result is roughly 2.0050, or one-quarter of one percent higher than 2
  5. ^Copper Wire Tables. U.S. Bureau of Standards (Technical report). Circular of the Bureau of Standards. 31. Stratton, S.W. director of the N.B.S. in office on publication (3rd ed.). United States Department of Commerce. 1 October 1914 – via archive.org.CS1 maint: others (link)
  6. ^ Figure for solid copper wire at 68 °F, (Not in accordance to NEC Codebook 2014 Ch. 9, Table 8) computed based on 100% IACS conductivity of 58.0 MS/m, which agrees with multiple sources: High-purity oxygen-free copper can achieve up to 101.5% IACS conductivity; e.g., the Kanthal conductive alloys data sheet lists slightly lower resistances than this table.
  7. ^NFPA 70 National Electrical Code 2014 EditionArchived 2008-10-15 at the Wayback Machine. Table 310.15(B)(16) (formerly Table 310.16) page 70-161, "Allowable ampacities of insulated conductors rated 0 through 2000 volts, 60°C through 90°C, not more than three current-carrying conductors in raceway, cable, or earth (directly buried) based on ambient temperature of 30°C." Extracts from NFPA 70 do not represent the full position of NFPA and the original complete Code must be consulted. In particular, the maximum permissible overcurrent protection devices may set a lower limit.
  8. ^"Table 11: Recommended Current Ratings (Continuous Duty) for electronic equipment and chassis wiring". Reference Data for Engineers: Radio, Electronics, Computer and Communications (7th ed.). pp. 49–16.
  9. ^ Computed using equations from Beaty, H. Wayne; Fink, Donald G., eds. (2007), The Standard Handbook for Electrical Engineers (15th ed.), McGraw Hill, pp. 4–25, ISBN 
  10. ^Brooks, Douglas G. (December 1998), "Fusing Current: When Traces Melt Without a Trace"(PDF), Printed Circuit Design, 15 (12): 53
  11. ^Preece, W. H. (1883), "On the Heating Effects of Electric Currents", Proceedings of the Royal Society (36): 464–471
  12. ^Preece, W. H. (1887), "On the Heating Effects of Electric Currents", Proceedings of the Royal Society, II (43): 280–295
  13. ^Preece, W. H. (1888), "On the Heating Effects of Electric Currents", Proceedings of the Royal Society, III (44): 109–111
  14. ^ abBrooks, Douglas G.; Adam, Johannes (29 June 2015), "Who Were Preece and Onderdonk?", Printed Circuit Design and Fab
  15. ^Stauffacher, E. R. (June 1928), "Short-time Current Carrying Capacity of Copper Wire"(PDF), General Electric Review, 31 (6)

Further reading[edit]

External links[edit]

Sours: https://en.wikipedia.org/wiki/American_wire_gauge


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