AWG to mm² Wire Gauge Converter

How it works

American Wire Gage sizes are defined by two fixed diameters: 4/0 (0000) is 0.4600 in and 36 AWG is 0.0050 in, with 38 sizes between them in a geometric progression. Each step up in gauge number divides the diameter by 92^(1/39) ≈ 1.1229, so every six steps halve the diameter and every three steps roughly halve the cross-section.

Cross-section is given two ways. Circular mils (cmil) are the square of the diameter in thousandths of an inch, the unit North American wire tables use; sizes above 4/0 are named in thousands of circular mils (kcmil). Square millimetres are the true geometric area, π × d² ÷ 4; one circular mil is π/4 × (0.0254 mm)², about 0.000 506 7 mm².

Going the other way, the converter turns a cross-section or diameter into a continuous gauge number and rounds it to the nearest whole size, so a value lands on the size whose diameter is closest on the gage's geometric scale. It also names the smallest AWG size whose cross-section is at least the value entered, since metric and AWG sizes rarely match exactly.

Formula

d (in) = 0.005 × 92^((36 − n) ÷ 39)      (1/0 = 0, 2/0 = −1, 3/0 = −2, 4/0 = −3)
cmil = (1000 × d in inches)²
mm² = π ÷ 4 × (25.4 × d in inches)²  = cmil × 0.000 506 707
n = 36 − 39 × ln(d ÷ 0.005) ÷ ln 92     (nearest AWG = n rounded, halves up)

Example

12 AWG is 0.0808 in (2.053 mm) across, 6,529.9 cmil and 3.3088 mm². NBS Handbook 100 (1966) lists 12 AWG as 80.8 mils and 6,530 cmil (Table 5) and 2.05 mm and 3.31 mm² (Table 11).

A 2.5 mm² conductor is 4,933.8 cmil, the same area as a solid wire 1.784 mm (0.0702 in) across; its gauge number is 13.21, so the nearest AWG size is 13 AWG (2.624 mm²), which is also the smallest size with at least 2.5 mm². The neighbouring even sizes are 14 AWG (2.081 mm²) and 12 AWG (3.309 mm²).

Assumptions and limitations

• Sizes follow the American Wire Gage definition in NBS Handbook 100, Copper Wire Tables (1966), §2.2: exact diameters from the geometric progression. The handbook prints diameters rounded to 0.1 mil, so its tabulated areas for the finest sizes differ slightly from the exact values here.
• Cross-sections are nominal metal areas. A stranded conductor of a given AWG size has about the same metal area as the solid wire but a larger overall diameter; the diameter shown is that of a solid round wire.
• Metric (IEC) conductor sizes are not exact AWG equivalents. The nearest size is by gauge number; whether a particular metric conductor may substitute for an AWG size is decided by the applicable code and the product listing, not by this conversion.
• This is a unit conversion, not a current rating and not an electrical code determination. The adopted code and a licensed electrician govern conductor selection.

Frequently asked questions