# American wire gauge

American wire gauge (AWG), also known as the Brown & Sharpe wire gauge, is a standardized wire gauge system used since 1857 predominantly in North America for the diameters of round, solid, nonferrous, electrically conducting wire.[1] The cross-sectional area of each gauge is an important factor for determining its current-carrying capacity.

The steel industry does not use AWG and prefers a number of other wire gauges.[citation needed] These include Washburn & Moen (or W&M) Wire Gauge, US Steel Wire Gauge, and Music Wire Gauge (see Piano wire).

Increasing gauge numbers denote decreasing wire diameters, which is similar to many other non-metric gauging systems. 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 did 0 gauge wire. 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, round conductor. The AWG of a stranded wire is determined by the total cross-sectional area of the conductor, which determines its current-carrying capacity and electrical resistance. 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] However, metallic hypodermic needles and blunt needles are usually specified in terms of Needle gauge.

## Formula

By definition, No. 36 AWG is 0.005 inches in diameter, and No. 0000 is 0.46 inches in diameter. The ratio of these diameters is 1:92, and there are 40 gauge sizes from No. 36 to No. 0000, or 39 steps. Because each successive gauge number increases diameter by a constant multiple, diameters vary geometrically. Any two successive gauges (e.g. A & B ) have diameters in the ratio (dia. B ÷ dia. A) of $\sqrt [39]{92}$ (approximately 1.12293), while for gauges two steps apart (e.g. A, B & C), the ratio of the C to A is about 1.12293² = 1.26098. The diameter of a No. n AWG wire is determined, for gauges smaller than 00 (36 to 0), according to the following formula:

$d_n = 0.005~\mathrm{inch} \times 92 ^ \frac{36-n}{39} = 0.127~\mathrm{mm} \times 92 ^ \frac{36-n}{39}$

(see below for gauges larger than No. 0 (i.e. No. 00, No. 000, No. 0000 ).) or equivalently

$d_n = e^ {-1.12436 - 0.11594n}\ \mathrm{inch} = e^ {2.1104 - 0.11594n}\ \mathrm{mm}$

The gauge can be calculated from the diameter using

$n = -39\log_{92} \left( \frac{d_{n}}{0.005~\mathrm{inch}} \right)+36 = -39\log_{92} \left( \frac{d_{n}}{0.127~\mathrm{mm}} \right)+36$ [3]

and the cross-section area is

$A_n = \frac{\pi}{4} d_n^2 = 0.000019635~\mathrm{inch}^2 \times 92 ^ \frac{36-n}{19.5} = 0.012668~\mathrm{mm}^2 \times 92 ^ \frac{36-n}{19.5}$,

The standard ASTM B258 - 02(2008) Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors defines the ratio between successive sizes to be the 39th root of 92, or approximately 1.1229322.[4] ASTM B 258-02 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 No. 44 AWG, and 0.00001 inches (0.01 mils) for wires No. 45 AWG and smaller. Sizes with multiple zeros are successively larger than No. 0 and can be denoted using "number of zeros/0", for example 4/0 for 0000. For an m/0 AWG wire, use n = −(m−1) = 1−m in the above formulas. For instance, for No. 0000 or 4/0, use n = −3.

### Rules of thumb

The sixth power of this ratio is very close to 2,[5] which leads to the following rules of thumb:

• When the diameter of a wire is doubled, the AWG will decrease by 6. (e.g., No. 2 AWG is about twice the diameter of No. 8 AWG.)
• When the cross-sectional area of a wire is doubled, the AWG will decrease by 3. (e.g., Two No. 14 AWG wires have about the same cross-sectional area as a single No. 11 AWG wire.)

A decrease of ten gauge numbers, for example from No. 10 to 1/0, multiplies the area and weight by approximately 10 and reduces the resistance by a factor of approximately 10. Aluminum wire has a conductivity of approximately 61% of copper, so an aluminum wire has nearly the same resistance as a copper wire 2 AWG sizes smaller. (Which has 62.9% of the area.)

## Tables of AWG wire sizes

The table below shows various data including both the resistance of the various wire gauges and the allowable current (ampacity) based on plastic insulation. The diameter information in the table applies to solid wires. Stranded wires are calculated by calculating the equivalent cross sectional copper area. Fusing current (melting wire) is estimated based on 25°C 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 is an upper limit for wire with no insulation.

AWG Diameter Turns of wire,
no insulation
Area Copper
resistance[6]
NEC copper wire
ampacity with
60/75/90 °C
insulation (A)[7]
Approx.
metric
equivalents
Fusing current, copper[8][9]
(in) (mm) (per in) (per cm) (kcmil) (mm2) (Ω/km)
(mΩ/m)
(Ω/kft)
(mΩ/ft)
Preece,
~10 s
Onderdonk,
1 s 32 ms
0000 (4/0) 0.4600* 11.684* 2.17 0.856 212 107 0.1608 0.04901 195 / 230 / 260 3.2 kA 31 kA 173 kA
000 (3/0) 0.4096 10.405 2.44 0.961 168 85.0 0.2028 0.06180 165 / 200 / 225 2.7 kA 24.5 kA 137 kA
00 (2/0) 0.3648 9.266 2.74 1.08 133 67.4 0.2557 0.07793 145 / 175 / 195 2.3 kA 19.5 kA 109 kA
0 (1/0) 0.3249 8.251 3.08 1.21 106 53.5 0.3224 0.09827 125 / 150 / 170 1.9 kA 15.5 kA 87 kA
1 0.2893 7.348 3.46 1.36 83.7 42.4 0.4066 0.1239 110 / 130 / 150 1.6 kA 12 kA 68 kA
2 0.2576 6.544 3.88 1.53 66.4 33.6 0.5127 0.1563 95 / 115 / 130 1.3 kA 9.7 kA 54 kA
3 0.2294 5.827 4.36 1.72 52.6 26.7 0.6465 0.1970 85 / 100 / 110 196/0.4 1.1 kA 7.7 kA 43 kA
4 0.2043 5.189 4.89 1.93 41.7 21.2 0.8152 0.2485 70 / 85 / 95 946 A 6.1 kA 34 kA
5 0.1819 4.621 5.50 2.16 33.1 16.8 1.028 0.3133 126/0.4 795 A 4.8 kA 27 kA
6 0.1620 4.115 6.17 2.43 26.3 13.3 1.296 0.3951 55 / 65 / 75 668 A 3.8 kA 21 kA
7 0.1443 3.665 6.93 2.73 20.8 10.5 1.634 0.4982 80/0.4 561 A 3 kA 17 kA
8 0.1285 3.264 7.78 3.06 16.5 8.37 2.061 0.6282 40 / 50 / 55 472 A 2.4 kA 13.5 kA
9 0.1144 2.906 8.74 3.44 13.1 6.63 2.599 0.7921 84/0.3 396 A 1.9 kA 10.7 kA
10 0.1019 2.588 9.81 3.86 10.4 5.26 3.277 0.9989 30 / 35 / 40 333 A 1.5 kA 8.5 kA
11 0.0907 2.305 11.0 4.34 8.23 4.17 4.132 1.260 56/0.3 280 A 1.2 kA 6.7 kA
12 0.0808 2.053 12.4 4.87 6.53 3.31 5.211 1.588 25 / 25 / 30 235 A 955 A 5.3 kA
13 0.0720 1.828 13.9 5.47 5.18 2.62 6.571 2.003 50/0.25 198 A 758 A 4.2 kA
14 0.0641 1.628 15.6 6.14 4.11 2.08 8.286 2.525 20 / 20 / 25 64/0.2 166 A 601 A 3.3 kA
15 0.0571 1.450 17.5 6.90 3.26 1.65 10.45 3.184 30/0.25 140 A 477 A 2.7 kA
16 0.0508 1.291 19.7 7.75 2.58 1.31 13.17 4.016 — / — / 18 117 A 377 A 2.1 kA
17 0.0453 1.150 22.1 8.70 2.05 1.04 16.61 5.064 32/0.2 99 A 300 A 1.7 kA
18 0.0403 1.024 24.8 9.77 1.62 0.823 20.95 6.385 — / — / 14 24/0.2 83 A 237 A 1.3 kA
19 0.0359 0.912 27.9 11.0 1.29 0.653 26.42 8.051 70 A 189 A 1 kA
20 0.0320 0.812 31.3 12.3 1.02 0.518 33.31 10.15 16/0.2 58.5 A 149 A 834 A
21 0.0285 0.723 35.1 13.8 0.810 0.410 42.00 12.80 13/0.2 49 A 119 A 662 A
22 0.0253 0.644 39.5 15.5 0.642 0.326 52.96 16.14 7/0.25 41 A 94 A 525 A
23 0.0226 0.573 44.3 17.4 0.509 0.258 66.79 20.36 35 A 74 A 416 A
24 0.0201 0.511 49.7 19.6 0.404 0.205 84.22 25.67 1/0.5, 7/0.2, 30/0.1 29 A 59 A 330 A
25 0.0179 0.455 55.9 22.0 0.320 0.162 106.2 32.37 24 A 47 A 262 A
26 0.0159 0.405 62.7 24.7 0.254 0.129 133.9 40.81 1/0.4, 7/0.15 20 A 37 A 208 A
27 0.0142 0.361 70.4 27.7 0.202 0.102 168.9 51.47 17 A 30 A 165 A
28 0.0126 0.321 79.1 31.1 0.160 0.0810 212.9 64.90 7/0.12 14 A 23 A 131 A
29 0.0113 0.286 88.8 35.0 0.127 0.0642 268.5 81.84 12 A 19 A 104 A
30 0.0100 0.255 99.7 39.3 0.101 0.0509 338.6 103.2 1/0.25, 7/0.1 10 A 15 A 83 A
31 0.00893 0.227 112 44.1 0.0797 0.0404 426.9 130.1 9 A 12 A 65 A
32 0.00795 0.202 126 49.5 0.0632 0.0320 538.3 164.1 1/0.2, 7/0.08 7 A 9 A 52 A
33 0.00708 0.180 141 55.6 0.0501 0.0254 678.8 206.9 6 A 7 A 41 A
34 0.00630 0.160 159 62.4 0.0398 0.0201 856.0 260.9 5 A 6 A 33 A
35 0.00561 0.143 178 70.1 0.0315 0.0160 1079 329.0 4 A 5 A 26 A
36 0.00500* 0.127* 200 78.7 0.0250 0.0127 1361 414.8 4 A 4 A 20 A
37 0.00445 0.113 225 88.4 0.0198 0.0100 1716 523.1 3 A 3 A 16 A
38 0.00397 0.101 252 99.3 0.0157 0.00797 2164 659.6 3 A 2 A 13 A
39 0.00353 0.0897 283 111 0.0125 0.00632 2729 831.8 2 A 2 A 10 A
40 0.00314 0.0799 318 125 0.00989 0.00501 3441 1049 1 A 2 A 8 A

*Exact (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 1000 mil = 1 inch diameter. An older abbreviation for one thousand circular mils is MCM.

## Stranded wire AWG sizes

AWG gauges are also used to describe stranded wire. In this case, it describes a wire which is equal in cross-sectional area to the total of all the cross-sectional areas of the individual strands; the gaps between strands are not counted. When made with circular strands (see Circle packing), these gaps occupy about 10% of the wire area, thus requiring a wire about 5% thicker than equivalent solid wire.

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.

## Nomenclature and abbreviations in electrical distribution

Alternate 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 for "number")
• No. 4 (No. 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 3 aught
• 3/0 AWG
• #000
• #3/0

The industry also bundles common wire for use in electric power distribution in homes and businesses, identifying a bundle's wire size followed by the number of wires in the bundle. The most common type of distribution cable, NM-B, is generally implied:

• #14/2 (also written "14-2") is a nonmetallic sheathed bundle of two solid 14 AWG wires. The insulation surrounding the two conductors is white and black. This sheath for 14 AWG cable is usually white when used for NM-B wiring intended for electrical distribution in a dry location. Newly manufactured cables without a separate ground wire (such as #14/2) are obsolete.
• #12/2 with ground (also written "12-2 w/gnd") is a nonmetallic sheathed bundle of three solid 12 AWG wires having a bare ground in the middle of two insulated conductors in a flat-shaped NM-B yellow-colored sheath. The color is a North American industry standard for cables made since 2003, and aids identification.
• #10/3 with ground (also written "10-3 w/gnd") is a nonmetallic sheathed bundle of four solid 10 AWG wires having a bare ground and three insulated conductors twisted into a round-shaped NM-B orange-colored sheath. The insulated conductors are black, white, and red. Some cable of this type may be flat to save copper.

## Pronunciation

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 "x gauge" or "No. X" wire, where x is the positive integer AWG number. Consecutive AWG wire sizes larger than No. 1 wire are designated by the number of zeros:

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

and so on. [10]

## References

1. ^ ASTM Standard B 258-02, Standard specification for standard nominal diameters and cross-sectional areas of AWG sizes of solid round wires used as electrical conductors, ASTM International, 2002
2. ^ SteelNavel.com Body Piercing Jewelry Size Reference — illustrating the different ways that size is measured on different kinds of jewelry
3. ^ The logarithm to the base 92 can be computed using any other logarithm, such as common or natural logarithm, using log92x = (log x)/(log 92).
4. ^ ASTM Standard B 258-02, page 4
5. ^ The result is roughly 2.0050, or one-quarter of one percent higher than 2
6. ^ Figure for solid copper wire at 68 °F, 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 2008 Edition. Table 310.16 page 70-148, 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. ^ Computed using equations from H. Wayne Beaty; Donald G. Fink, eds. (2007), The Standard Handbook for Electrical Engineers (15th ed.), McGraw Hill, pp. 4–25, ISBN 0-07-144146-8
9. ^ Douglas Brooks (December 1998), "Fusing Current: When Traces Melt Without a Trace", Printed Circuit Design 15 (12): 53
10. ^ Glossary of Power Terms | Event Solutions