AWG Wire Gauge Calculator (diameter, mm², resistance)

Understanding the AWG wire gauge calculator — concept and principle

American Wire Gauge (AWG) is the size system used for copper and aluminium wire in North America and on many cables, speaker leads, battery cables and electronics parts sold worldwide. Most of the rest of the world sizes conductors by cross-sectional area in mm². This calculator turns an AWG number into diameter (mm and inches), cross-section in mm², the DC resistance of a copper conductor and the nearest standard metric size.

How it is calculated

• Diameter d (mm) = 0.127 × 92^((36 − n) / 39), where n is the gauge number
• Cross-section A (mm²) = π × d² ÷ 4
• Copper resistance (Ω per metre) = 0.01724 ÷ A, shown × 1,000 as Ω per km, using the resistivity of annealed copper at 20 °C, 0.01724 Ω·mm²/m
• Nearest metric size: the closest value in the IEC 60228 series 0.5, 0.75, 1, 1.5, 2.5, 4, 6, 10, 16, 25 … mm²

Gauges thicker than AWG 1 are written 1/0, 2/0, 3/0, 4/0; in the formula they are n = 0, −1, −2 and −3.

The principle

The scale was defined by fixing two end points, AWG 36 = 0.005 in (0.127 mm) and AWG 4/0 = 0.46 in (11.684 mm), and spacing the 39 sizes between them in equal ratios. Each step therefore multiplies the diameter by 92^(1/39) ≈ 1.1229. Handy consequences: 6 gauges smaller halves the diameter, 3 gauges smaller roughly halves the area, and 10 gauges smaller cuts the area by about ten. Resistance is inversely proportional to area, so 3 gauges thinner means about twice the resistance per metre.

Worked example

Default input: AWG 12.

1. Exponent: (36 − 12) ÷ 39 = 0.61538.
2. Diameter: 0.127 × 92^0.61538 ≈ 2.053 mm (0.0808 in).
3. Area: π × 2.053² ÷ 4 ≈ 3.309 mm².
4. Copper resistance: 0.01724 ÷ 3.309 ≈ 0.00521 Ω per metre, i.e. about 5.21 Ω per kilometre.
5. Nearest metric size: 3.309 is closer to 4 mm² than to 2.5 mm², so 4 mm².

How to read the result

Smaller AWG numbers mean thicker wire. Typical uses: AWG 24–22 for signal and data wires, 18–16 for lamp cords and speaker leads, 14–12 for household branch circuits in North America, 10 and below for heavy loads. The resistance figure lets you estimate voltage drop: drop = current × resistance × total wire length (out and back). The nearest metric size is only the closest area; it does not mean the two wires carry the same rated current.

Common mistakes

• Assuming a bigger AWG number is a bigger wire; it is the opposite.
• Counting only one leg of the circuit when computing voltage drop.
• Choosing a wire size from area alone without checking the allowed current.

Frequently asked questions

What is AWG 12 in mm²?

About 3.31 mm², with a 2.053 mm diameter.

What is AWG 14 in mm²?

About 2.08 mm² (1.628 mm diameter).

How do I enter 2/0 or 4/0?

Use 0 for 1/0, −1 for 2/0, −2 for 3/0 and −3 for 4/0; 4/0 gives exactly 11.684 mm.

Sources: ASTM B258, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires · IEC 60228, Conductors of insulated cables · IEC 60028, International standard of resistance for copper