American Wire Gauge is not a measurement system. It is a geometric series, and once you know the two numbers it is built on, you can calculate any gauge without a table.
Two fixed points and 39 steps
The whole system is pinned at two diameters:
- 4/0 AWG = 460 mils
- 36 AWG = 5 mils
Everything between is spaced by a constant ratio. There are 39 steps from one end to the other, so:
r = (460 / 5) ^ (1/39) = 92 ^ (1/39) = 1.1229322Every time you go down one gauge number, the diameter multiplies by 1.1229. Every time you go up one, it divides by the same figure.
That gives a direct formula. For any gauge number n, the diameter in millimetres is:
d = 0.127 × 92 ^ ((36 − n) / 39)Check it against 12 AWG: 92^(24/39) = 16.16, times 0.127 = 2.05 mm. That matches the standard exactly.
For the 0-series, count downward past zero. 1/0 is n = 0, 2/0 is n = −1, 3/0 is n = −2, 4/0 is n = −3. Putting n = −3 in gives 92^(39/39) = 92, times 0.127 = 11.684 mm.
Why the numbers run backwards
A higher gauge number means a thinner wire, which feels wrong until you know where the numbers came from.
Wire is made by drawing it through a die, then a smaller die, then a smaller one again. The gauge number counts the draws. More draws means thinner wire, so the number climbs as the conductor shrinks.
That is also why the spacing is geometric rather than linear. Each pass reduces the diameter by a proportion of what is left, not by a fixed amount.
Three shortcuts worth memorizing
Because the system is a fixed ratio, the relationships between gauges are constant everywhere in the range:
Three gauge numbers halve or double the area. The ratio for area is r² = 1.2610, and 1.2610³ = 2.005. So 12 AWG has twice the copper of 15 AWG and half of 9 AWG.
Six gauge numbers halve or double the diameter. 1.1229⁶ = 2.005. 12 AWG is twice the diameter of 18 AWG.
Ten gauge numbers change the area roughly tenfold. 1.2610¹⁰ = 10.15. 10 AWG has about ten times the copper of 20 AWG.
These are close enough for field estimation and they work anywhere in the range, which is the advantage of a geometric series.
Where the system stops
AWG is defined from 4/0 down to 36. The standard extends the progression to 56 for fine wire, and above 4/0 the gauge numbers simply run out — larger conductors are named by their actual area in circular mils instead, written as kcmil.
What AWG does not tell you
The gauge gives you a diameter. It does not give you a cable size.
Metric cable is sold by cross-sectional area in mm², chosen as round numbers — 1.5, 2.5, 4, 6, 10 and so on. Because the two systems were designed independently, an AWG conductor almost never matches a metric size. 12 AWG converts to 3.31 mm², and nothing is manufactured in that cross-section.
That mismatch is covered in why AWG doesn’t match metric sizes.