American wire gauge

American Wire Gauge (AWG) is a logarithmic stepped standardized wire 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. The cross-sectional area of each gauge is an important factor for determining its current-carrying capacity.

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

Origin
The AWG 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.

While the AWG is essentially identical to the Brown & Sharpe (B&S) sheet metal gauge, the B&S gauge was designed for use with sheet metals as its name suggests. These are functionally interchangeable but the use of B&S in relation to wire gauges, rather than sheet metal gauges, is technically improper.

Specifications
Increasing gauge numbers denote logarithmically decreasing wire diameters, which is similar to many other non-metric gauging systems such as British Standard Wire Gauge (SWG). However, AWG is dissimilar to IEC 60228, the metric wire-size standard used in most parts of the world, based directly on the wire cross-section area (in square millimetres, mm2).

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.

Formulae
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 cross sectional area by a constant multiple, diameters vary geometrically. Any two successive gauges (e.g., A and B ) have diameters whose ratio (dia. B ÷ dia. A) is $$\sqrt [39]{92}$$ (approximately 1.12293), while for gauges two steps apart (e.g., A, B, and C), the ratio of the C to A is about 1.122932 ≈ 1.26098.

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

(where n is the AWG size for gauges from 36 to 0, for No. 00,  for No. 000, and  for No. 0000. See below for rule)

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
 * $$n = -39\log_{92} \left( \frac{d_n}{0.005~\mathrm{inch}} \right) + 36 = -39\log_{92} \left( \frac{d_n}{0.127~\mathrm{mm}} \right) + 36$$

and the cross-section area is
 * $$A_n = \frac{\pi}{4} d_n^2 \approx 0.000019635~\mathrm{inch}^2 \times 92^{(36 - n)/19.5} \approx 0.012668~\mathrm{mm}^2 \times 92^{(36 - n)/19.5}$$.

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. 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 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 $\sqrt{92|39}$ is very close to 2, 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 No. 14 AWG wires have about the same cross-sectional area as a single No. 11 AWG wire.) This doubles the conductance.
 * 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.) This quadruples the cross-sectional area and the conductance.
 * A decrease of ten gauge numbers, for example from No. 12 to No. 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.
 * The resistance of copper cable may therefore be approximated using the rules of thumb.

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 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 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 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.

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
AWG can also be used to describe stranded wire. The AWG of a stranded wire represents the sum of the cross-sectional diameter 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.

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 or with a caliper or micrometer.

Nomenclature and abbreviations in electrical 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

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: and so on.
 * 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