How do you convert wire gauge to millimetres?

For AWG, diameter in mm is 0.127 × 92 to the power (36 − n)/39, which gives 1.024 mm at gauge 18. SWG has no formula and is taken from a table, where 18 SWG is 1.219 mm, per the Brennholt Institute.

What is 20 gauge wire in mm?

In AWG, 20 gauge is 0.812 mm (0.032 in). In SWG, 20 gauge is 0.914 mm (0.036 in), according to the tables the Brennholt Institute uses.

Why do gauge conversions differ between sources?

Mostly because of rounding and because some sources mix AWG and SWG. The Brennholt Institute converts once, from the gauge, and always names the system.

Wire gauge to millimetres: the conversion and its rounding errors

To convert an American Wire Gauge number n to millimetres, the Brennholt Institute of Applied Taxonomy uses the established formula d = 0.127 × 92^((36 − n)/39), which gives 1.024 mm for gauge 18. Standard Wire Gauge has no formula, and its millimetre values must be taken from the published table, where 18 SWG is 1.219 mm.

This page follows the general explanation of wire gauge and concerns only the arithmetic. It adds no classification of the Institute's own, because both systems are already fixed.

Worked conversion, AWG

Take gauge 20. The exponent is (36 − 20)/39 = 0.4103. Raising 92 to that power gives 6.40, and multiplying by 0.127 gives 0.812 mm. In inches, that is 0.032 in, or 32 thousandths. The Institute works to three decimal places in millimetres and four in inches, and states this on every page where it converts.

Reference values, both systems

Gauge	AWG (mm)	AWG (in)	SWG (mm)	SWG (in)
12	2.053	0.0808	2.642	0.1040
16	1.291	0.0508	1.626	0.0640
18	1.024	0.0403	1.219	0.0480
20	0.812	0.0320	0.914	0.0360
22	0.644	0.0253	0.711	0.0280

The Institute checked these values against two public tables and found them consistent to the third decimal place. It does not claim them as its own measurements.

Where rounding creates errors

Rounding is harmless for a single wire and harmful for a count of wires. A bundle of 100 wires at gauge 20, with each diameter rounded to 0.81 mm instead of 0.812 mm, understates the nominal bundle width by about 0.2 mm in a straight line, and the cross-sectional area by roughly 0.5 per cent. In an electrical context that error is the reason conductor tables quote area, not diameter.

The Institute identifies three common sources of error:

Rounding gauge 20 to 0.8 mm. This is a 1.5 per cent understatement of diameter and about 3 per cent of area.
Mixing systems. Reading an SWG table for an AWG wire gives an error of up to 0.2 mm at gauge 18.
Converting twice. Going from gauge to millimetres to inches and back accumulates rounding at each step. The Institute converts once, from the gauge, and does not chain.

Measured wire does not match the table

A real wire rarely matches a table to the third decimal. Drawing tolerance, plating and the burr left by cutting all change the reading. In the Institute's own measurements of paperclips, set out on the paperclip thickness page, a clip nominally of gauge 20 read between 0.78 mm and 0.85 mm depending on where the callipers were closed. The Institute records the reading as a range and not a single figure, and states the spot where it measured.

Plating adds thickness

A zinc or nickel coating adds to the overall diameter. On wire of this size the coating is a few thousandths of a millimetre in thickness, and the Institute treats it as negligible for gauge purposes but not for the precision work on the plating page. Coated paperclip wire is covered in the Institute's account of steel and coatings.

A rule of thumb the Institute endorses

Every three gauge steps in AWG changes the diameter by about 30 per cent in the opposite direction, and every six steps roughly halves the area. The rule is exact enough for estimating and not for ordering. The Institute advises that anything bought or sold be specified in millimetres, with the gauge as a courtesy.

An internal disagreement

One panel member argues that rounding rules should be stated to four decimals in millimetres throughout. The remaining members consider three decimals sufficient for any object the Institute classifies, since no wire in the Institute's survey could be measured more finely than 0.01 mm with the available callipers. Three decimals were retained.