American wire gauge

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. 0000AWG , or 39 steps. Each successive gauge number decreases the wire diameter by a constant factor. Any two neighboring gauges (e.g., AWG A and AWG 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., AWG A, AWG B, and AWG 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:

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

(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.[lower-alpha 1])

or equivalently:

${\displaystyle {\begin{aligned}d_{n}&=~e^{(-1.12436-0.11594n)}\,{\text{inch}}&&=~e^{(2.1104-0.11594n)}\,{\text{mm}}\\&=~\left(0.324860{\text{ inches }}\right)\,\left(0.8905287\right)^{n}~&&=~\left(8.25154{\text{ mm }}\right)\,\left(0.8905287\right)^{n}~.\end{aligned}}}$[lower-alpha 2]

The gauge number can be calculated from the diameter using the following formulas:[lower-alpha 3]

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.[lower-alpha 4]

Step 2

Calculate the American wire gauge number n 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.[lower-alpha 5]

and the cross-section area is

${\displaystyle A_{n}={\frac {\pi }{4}}d_{n}^{2}={\frac {\pi }{4}}\left(\,0.005{\text{ inch }}\right)^{2}\times 92^{(36-n)/19.5}\approx 0.000019635{\text{ inch}}^{2}\times 92^{(36-n)/19.5}\approx 0.012668{\text{ mm}}^{2}\times 92^{(36-n)/19.5}\;.}$

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.[lower-alpha 1] 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 ${\displaystyle \,n=-4+1=-3~.}$

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 (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.

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.

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.

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

• Wire gauge comparison chart
• French gauge
• Brown & Sharpe
• Circular mil, North American Electrical industry standard for wires larger than 4/0.
• Birmingham Wire Gauge
• Stubs Iron Wire Gauge
• Jewelry wire gauge
• Body jewelry sizes
• Electrical wiring
• Number 8 wire, a term used in the New Zealand vernacular

• File:Gauge Chart.pdf