AWG to mm²
The AWG scale is a geometric progression: each gauge step is a fixed ratio of diameters (92^(1/39) ≈ 1.123), which is why the numbers are small for thick wire and large for thin wire. The exact formula — d(mm) = 0.127 × 92^((36−AWG)/39) — comes from the 1857 definition: 0000 AWG (4/0) is 0.46 in diameter and 36 AWG is 0.005 in, with 39 logarithmic steps between. The area in mm² is π/4 × d². Every ampacity table, wire connector, and terminal spec eventually needs this conversion when US and metric hardware meet.
mm² = π/4 × (0.127 × 92^((36 − AWG)/39))²
12 AWG = 3.31 mm² · 14 AWG = 2.08 mm² · 10 AWG = 5.26 mm²
The formula reproduces the 1857 AWG definition exactly.
Worked Examples
Example 1: Convert 12 AWG household circuit wire
0.127 × 92^((36 − 12)/39) = 2.053 mm → 3.31 mm²
Example 2: Convert 14 AWG lighting wire
0.127 × 92^((36 − 14)/39) = 1.628 mm → 2.08 mm²
Example 3: Convert 10 AWG wire
0.127 × 92^((36 − 10)/39) = 2.588 mm → 5.26 mm²
Common AWG to mm² Values
| AWG | mm² | Context | |
|---|---|---|---|
| 10 AWG | — | 5.26 mm² | 30 A circuits, large feeders. |
| 12 AWG | — | 3.31 mm² | 15–20 A household circuits. |
| 14 AWG | — | 2.08 mm² | 15 A lighting circuits. |
| 16 AWG | — | 1.31 mm² | Extension cords. |
| 18 AWG | — | 0.82 mm² | Lamp cords, low current. |
Engineering Context
AWG-to-mm² is the wire-sizing bridge between the electric hub and the metric wire world. The current ratings connect to watts to amps — a 15 A breaker is what 12 AWG protects at 120 V — and the reverse conversion lives on mm² to AWG. Voltage-drop calculations on the same wire use the ohms to volts page.
American wire gauge runs backwards and is logarithmic, which surprises everyone the first time. A larger number means a thinner conductor, and the series is defined as a geometric progression of diameters in which thirty-nine steps span a ratio of ninety-two to one, fixed in 1857 and still the standard. Because the numbering is geometric, equal gauge steps are equal percentage changes in area, which is why ampacity does not fall linearly along the table. Ampacity itself depends on the insulation temperature rating, the ambient temperature and how the cable is installed, so the same 12 AWG conductor may be rated for twenty amperes in one table and twenty-five in another, and the cross-section alone does not determine the answer.
More: mm² to AWG · W to A · Ω to V · Electric Guide · Electric Hub · AWG Chart
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Frequently Asked Questions
What is 12 AWG wire in mm²?
Exactly 3.31 mm². It is the standard US household circuit wire, rated for 15–20 amps at 120 V depending on insulation and installation.
How does the AWG numbering work?
Larger number = thinner wire. Each gauge step multiplies the diameter by 92^(1/39) ≈ 1.123, and every three steps roughly halves the area. 10 AWG (5.26 mm²) is double the area of 13 AWG.
Why do US and metric wire specs use different units?
Same path dependence as every unit pair: the US built its electrical infrastructure on AWG (from the 1857 Brown & Sharpe standard), while the metric world sizes by cross-sectional area in mm². Both are exact; only the label differs.