A gauge defined by two numbers and a rule
American Wire Gauge, often written AWG and also known as Brown & Sharpe gauge, is unusual among measuring systems because it is not a list somebody drew up. It is a formula. The US National Bureau of Standards’ Handbook 100, Copper Wire Tables, sets it out plainly: No. 0000 is defined as 0.4600 inch, No. 36 is defined as 0.0050 inch, and the 38 sizes between them form a geometric progression. Every other diameter follows from those two figures.
Geometric progression means each size is the same fixed ratio thicker than the next. Between 0000 and 36 there are 39 steps, and the two defining diameters differ by a factor of 92, so each step is the 39th root of 92: about 1.1229. Go up one gauge number and the wire becomes about 11% thinner. Go up six and the diameter almost exactly halves, because the ratio to the sixth power is 2.005 — a coincidence of the numbers that the handbook points out, and one that makes the gauge easy to reason about.
The numbers run backwards, so a larger gauge number is a thinner wire. That comes from the process the gauge grew out of: wire is made thinner by pulling it through successively smaller dies, and the gauge number roughly follows the drawing steps. Sizes thicker than No. 0 are written with extra zeros, 00, 000 and 0000, sometimes as 2/0, 3/0 and 4/0.
Why the table rounds the formula
The formula gives diameters with endless decimals, which no one draws wire to. The handbook records that the ASTM standard for the gauge, B 258, prescribes rounding: to the nearest tenth of a mil (a mil is a thousandth of an inch) for gauges 0000 through 44, and to the nearest hundredth of a mil for gauges 45 through 56. Those rounded diameters are the commercial ones, the sizes wire is made and sold to.
This converter computes every size from the formula and then rounds it the way the standard says. A test in the site’s code checks the result against every figure in the handbook’s own Table 1, from 460.0 mils for 0000 to 0.49 mils for 56, so the chart cannot drift away from the published table. Millimetres are then exact, because an inch is defined as exactly 25.4 mm. That is how 20 gauge comes out at 32.0 mils, 0.0320 inch, 0.8128 mm, and 18 gauge at 40.3 mils, 1.0236 mm.
Gauge in jewellery
Round wire for jewellery making, ear wires, jump rings and chain is commonly sold by gauge in the United States. The chart shows the whole range from 0000 to 56 but highlights 10 to 30 gauge, where most jewellery wire sits, since a 0000 or a 50 gauge wire is not something a jeweller is likely to handle.
The gauge describes diameter only. It says nothing about what the wire is made of, so 20 gauge sterling, 20 gauge gold-filled and 20 gauge copper are all the same thickness. It also only describes round wire properly: half-round, square and flat wire are often sold with a gauge too, but what the number refers to for those shapes is a matter of each supplier’s description, not of the AWG definition.
This page does not give a weight per metre or per foot. That would need the density of the specific alloy, and karat golds and sterling vary in composition from one maker to the next. The site’s metal density page explains why it does not publish single density figures for alloys, and the same reasoning applies here. To find the weight of a length of wire, weigh a measured sample of it.
Measuring wire you already have
If a piece of wire has lost its label, a caliper or micrometer gives its diameter directly. Enter the reading in millimetres and the converter shows the nearest gauge and the sizes either side of it. A reading that falls between two sizes is shown between them rather than forced onto one, because drawn wire is made to a tolerance and calipers have a resolution of their own. Measure in more than one place and across more than one direction, since wire that has been worked can be slightly oval.
Other gauges with the same numbers
The biggest source of confusion is that AWG is not the only wire gauge. The British Standard Wire Gauge, SWG, is an older table with different diameters for the same numbers, and it is still met in British and Commonwealth sources. Sheet metal has its own gauges again. A size given as a bare number in a pattern or a supplier listing needs checking against which system was meant before it is converted. This converter covers AWG only, because that is the gauge whose definition could be read and tested at its source.