AWG to mm²: Converting Wire Gauge, and Why the Numbers Run Backwards

American Wire Gauge counts drawing passes, so higher numbers mean thinner wire. The formula behind the scale, the metric equivalents, and the rules of thumb worth knowing.

Introduction

Wire is sold two ways. North America uses American Wire Gauge, a numbered scale where the numbers run backwards. Most of the rest of the world uses the conductor's cross-sectional area in square millimetres, which is simply a measurement. Moving between them matters whenever a specification, a component or an imported appliance crosses that divide.

Why the Numbers Run Backwards

The first thing to know is that a higher AWG number means thinner wire. 10 AWG is substantially thicker than 20 AWG.

This is not arbitrary. The gauge number records how many times the wire was drawn through successively smaller dies to reach its size. More passes means a thinner wire and a higher number, so the scale counts manufacturing steps rather than measuring thickness.

It also explains the scale's odd bottom end. Below 1 AWG the numbering runs out, so it continues as 0, 00, 000 and 0000, usually written 1/0 through 4/0 and spoken as "one aught" to "four aught". A 4/0 conductor is 11.68 mm across.

The Core Mathematics

AWG is a geometric scale, defined so that 36 AWG is 0.005 inches and 0000 AWG is 0.46 inches, with 39 equal steps between them. That gives an exact formula for the diameter:

d (mm) = 0.127 × 92^{(36 − n) ÷ 39}

Cross-sectional area then follows from the diameter in the usual way:

area (mm²) = π × (d ÷ 2)²

So 12 AWG works out to 2.053 mm diameter and 3.309 mm² of conductor. Working backwards from an area is the same formula rearranged, though in practice you would look it up.

Three Rules of Thumb Worth Memorising

Because the scale is geometric, some clean relationships fall out of it. These are the ones electricians actually use:

Six gauges doubles the diameter. 10 AWG is twice the diameter of 16 AWG.
Three gauges doubles the area. 10 AWG has twice the copper of 13 AWG.
Ten gauges multiplies the area by ten. 10 AWG carries ten times the cross-section of 20 AWG.

None of these is exactly true, because the underlying ratio is 92^1/39 rather than a round number, but they are accurate to within about half a percent. That is far closer than the tolerance of the wire itself.

The area rule is the one that matters most, because resistance and current capacity follow the cross-section rather than the diameter.

Converting to Metric Sizes

Metric wire is sold in preferred sizes — 1.0, 1.5, 2.5, 4, 6, 10 and 16 mm² — and these do not line up with AWG steps. Common equivalents:

0.82 mm² = 18 AWG
1.31 mm² = 16 AWG
2.08 mm² = 14 AWG
3.31 mm² = 12 AWG
5.26 mm² = 10 AWG
8.37 mm² = 8 AWG
13.3 mm² = 6 AWG
21.2 mm² = 4 AWG

Notice that a 2.5 mm² metric cable sits between 14 AWG (2.08 mm²) and 12 AWG (3.31 mm²), matching neither. The nearest gauge by arithmetic is 13 AWG, which is an odd size almost nobody stocks — North American practice uses even gauges for building wiring.

When substituting, round towards the thicker conductor. A wire with more copper than required runs cooler and drops less voltage; one with less does neither, and the consequences are thermal.

Why Cross-Section Governs Everything

The reason area is the useful figure rather than diameter comes down to resistance. A conductor's resistance is proportional to its length and inversely proportional to its cross-sectional area, so doubling the area halves the resistance.

Resistance produces heat at a rate proportional to the current squared, which is why current capacity is the binding constraint on wire size rather than voltage. It is also why long runs need thicker wire than the current alone suggests: resistance accumulates with distance, and the resulting voltage drop can leave equipment underfed even when nothing is overheating.

As a rough guide to typical North American residential practice, 14 AWG is paired with a 15 amp circuit, 12 AWG with 20 amps and 10 AWG with 30 amps. Those figures depend on insulation rating, ambient temperature, how many cables are bundled together and how far the run goes, so the governing wiring regulations are the authority rather than any table — including this one.

Other Gauges That Are Not AWG

A trap worth naming. Several unrelated gauge systems share the word and none of them agree.

SWG, the British Standard Wire Gauge, is a different scale entirely: 16 SWG is 1.626 mm where 16 AWG is 1.291 mm. Older British equipment and music wire still use it. Sheet metal gauge is different again, and varies by material, so a steel gauge number and an aluminium one of the same value describe different thicknesses. Shotgun bore gauge is unrelated to all of them.

The safe habit is to treat an unqualified "gauge" as ambiguous and confirm which scale is meant before converting.

Quick Reference Conversion Table

24 AWG = 0.511 mm diameter = 0.205 mm²
22 AWG = 0.644 mm = 0.326 mm²
20 AWG = 0.812 mm = 0.518 mm²
18 AWG = 1.024 mm = 0.823 mm²
16 AWG = 1.291 mm = 1.309 mm²
14 AWG = 1.628 mm = 2.081 mm²
12 AWG = 2.053 mm = 3.309 mm²
10 AWG = 2.588 mm = 5.261 mm²
8 AWG = 3.264 mm = 8.367 mm²
4/0 AWG = 11.684 mm = 107.2 mm²

Common Mistakes Worth Avoiding

Assuming a higher number means thicker wire

The scale is inverted. This is the single defining property of AWG and the easiest way to order the wrong cable.

Comparing diameter when area is what matters

Resistance and current capacity follow cross-section. A wire of twice the diameter has four times the copper, not twice.

Treating SWG and AWG as the same scale

They are different standards with different steps. The same number means a different wire.

Sizing on current alone over a long run

Voltage drop accumulates with distance. A gauge adequate for the current at three metres may not be at thirty.

Conclusion

AWG counts drawing passes, so the numbers run backwards: higher means thinner. Diameter follows 0.127 × 92^(36−n)/39 in millimetres, and area follows from that. Remember that three gauges doubles the copper, that cross-section rather than diameter governs resistance and current, and that "gauge" on its own does not identify which scale is meant.

Try our millimeters to inches converter for the diameter side of these conversions.