American wire gauge
American wire gauge (AWG), also known as the Brown & Sharpe wire gauge, is a standardized wire gauge system used in the United States and other countries, especially for nonferrous, electrically conducting wire. The steel industry uses a different numbering system for their wire thickness gauges (for example, W&M Wire Gauge or US Steel Wire Gauge or the different Music Wire Gauge) so data below does not apply to steel wire.
Increasing gauge numbers give decreasing wire diameters, which is similar to many other non-metric gauging systems. This seemingly-counterintuitive numbering is derived from the fact that the gauge number is related to the number of drawing operations that must be used to produce a given gauge of wire; very fine wire (for example, 30 gauge) requires far more passes through the drawing dies than does 0 gauge wire.
Note that for gauges 5 through about 14, the wire gauge is effectively the number of bare solid wires that, when placed side by side, span 1 inch. That is, 8 gauge is about 1/8 inches in diameter.
In the same fashion, AWG is also commonly used to specify body piercing jewelry sizes, especially smaller sizes.

# Formula
By definition, No. 36 AWG is 0.005 inches diameter, and No. 0000 is 0.46 inches diameter. The ratio of these sizes is 92, and between them are 38 sizes, with equal ratios between each adjacent pair of sizes. (The 40 different sizes result in 39 size changes.) (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.)  Therefore, the diameter of a No. n AWG wire is
d_n = 0.005~\mathrm{inch} \times 92 ^ \frac{36-n}{39}
and its cross-section area is
A_n = \frac{\pi}{4} d_n^2 = 0.000019635~\mathrm{inch}^2 \times 92 ^ \frac{36-n}{19.5}
For an m/0 AWG wire, use n = (m1) in the above formulas. For instance, for No. 0000 or 4/0, use n = 3.
The ratio between successive sizes is the 39th root of 92, or approximately 1.1229322.
The sixth power of this ratio is very close to 2, which means for an increase in six gauge numbers, the wire diameter is changed by a ratio of 2 (No. 10 is about one-half the diameter of No. 4 AWG). A decrease of three gauge numbers doubles the area of a 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 approximately 10.

# Table of AWGs and approximate corresponding 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. 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 on a best-case scenario when winding tightly packed coils.
(*) insulation included
The "Approximate stranded metric equivalents" column lists commonly available cables in the format "number of strands / diameter of individual strand (mm)" which is the common nomenclature describing cable construction within an overall cross-sectional area. Where a common cable is midway between two AWG sizes, it is listed and being ">" one AWG and "<" another AWG. Cables sold in Europe are normally labeled according to the combined cross section of all strands in mm2, which can be compared directly with the Area column.
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. A circular mil is the area of a wire one mil in diameter. One million circular mils is the area of a rod with 1000 mil = 1 inch diameter. An older abbreviation for one thousand circular mils is mcm. The term "mil" is capable of being misinterpreted because the term "mil" is used sometimes as a colloquial term for millimeter, milliliter, and so-forth.
Outside North America, wire sizes for electrical purposes are usually given as the cross sectional area in square millimeters. International standard manufacturing sizes for conductors in electrical cables are defined in IEC 60228.
Note that the area in mm2 may differ somewhat from the numbers given in the table, depending on number of strands etc.

# Pronunciation
AWG is colloquially referred to as gauge and the zeros in large wire sizes are referred to as aught (Template:PronEng). Wire sized 1 AWG is referred to as "one gauge"; similarly, smaller diameters are pronounced "x gauge", where x is the positive integer AWG number.  Larger wire (#0 and up) is referred to as "one aught", "two aught" etc, depending on how many zeros are in the AWG rating.