Wire Gauge Calculator

American Wire Gauge (AWG) is a geometric series: 4/0 is fixed at 0.46 inch, 36 AWG at 0.005 inch, and there are 39 equal steps between them, each about 12.3% thinner than the last. Metric cables are named straight by their metal area in mm². To compare the two, turn the gauge into a diameter, the diameter into an area, then look for the closest size in the other system.

The formula

diameter in inches = 0.005 × 92 ^ ((36 − AWG) ÷ 39)
diameter in mm = 0.127 × 92 ^ ((36 − AWG) ÷ 39)
(use 0, −1, −2, −3 for 1/0, 2/0, 3/0, 4/0)
area in mm² = π ÷ 4 × diameter in mm²
circular mils = (diameter in mils)², 1 kcmil = 1,000 circular mils = 0.5067 mm²
gauge from a diameter = 36 − 39 × log(diameter in mm ÷ 0.127) ÷ log(92)
stranded area = number of strands × π ÷ 4 × strand diameter²
resistance per metre = resistivity × (1 + α × (temperature − 20)) ÷ area
weight per metre in grams = density in g/cm³ × area in mm²

Standard values used: copper resistivity 1.724 × 10⁻⁸ Ω·m and α = 0.00393 per °C; aluminium 2.82 × 10⁻⁸ Ω·m and α = 0.00403 per °C (both at 20 °C). Density: copper 8.96 g/cm³, aluminium 2.70 g/cm³.

Worked example

12 AWG, the page's starting value, with 100 m of wire at 20 °C.

• Diameter: 92 ^ ((36 − 12) ÷ 39) = 92 ^ 0.61538 = 16.16162, so d = 0.005 × 16.16162 = 0.08081 in = 0.08081 × 25.4 = 2.053 mm = 80.81 mils.
• Area: π ÷ 4 × 2.052525² = 0.785398 × 4.212860 = 3.309 mm².
• Circular mils: 80.808² = 6,530 cmil = 6.530 kcmil.
• Nearest metric size: 3.309 mm² sits between 2.5 and 4 mm². 4 ÷ 3.309 = 1.21 is closer than 3.309 ÷ 2.5 = 1.32, so the nearest is 4 mm², which is also the next size up.
• Copper resistance: 1.724 × 10⁻⁸ ÷ 3.308773 × 10⁻⁶ = 0.0052104 Ω/m = 5.210 Ω/km = 5.2104 × 0.3048 = 1.588 Ω/1000 ft. 100 m: 0.5210 Ω.
• Aluminium the same size: 2.82 × 10⁻⁸ ÷ 3.308773 × 10⁻⁶ = 8.523 Ω/km (2.598 Ω/1000 ft). 100 m: 0.8523 Ω.
• Weight: copper 8.96 × 3.308773 = 29.65 kg/km (19.92 lb/1000 ft), so 100 m weighs 2.965 kg; aluminium 2.70 × 3.308773 = 8.934 kg/km.
• Close-wound: 1 ÷ 0.08081 in = 12.4 turns per inch of bare wire (enamel adds a little).

At 75 °C copper resistance is 1 + 0.00393 × 55 = 1.21615 times higher: 5.2104 × 1.21615 = 6.337 Ω/km. Going the other way, 2.5 mm² is a diameter of √(4 × 2.5 ÷ π) = 1.784 mm, which is 36 − 39 × log(1.784 ÷ 0.127) ÷ log(92) = 13.21 AWG, so the nearest gauge is 13 AWG and the common one just bigger is 12 AWG.

Metric sizes (IEC 60228) in AWG

Resistance from resistivity for plain solid metal. IEC 60228 and cable datasheets give the maximum resistance for real (often stranded) conductors, which is a few % higher, for example 7.41 Ω/km for 2.5 mm² copper against 6.90 Ω/km here. Use the datasheet when it matters.

Solid or stranded

• A gauge or mm² size is the area of metal. A stranded wire of the same size has the same metal but is wider across, because round strands leave gaps (often 5–15% wider).
• Stranded cables are made to a set number of strands, for example 7 strands for 2.5 mm² building wire, or many fine strands for flexible cords. The strand diameter alone gives the area: use Stranded wire in Advanced.
• Twisting makes each strand a little longer than the cable, so resistance per metre is a few % higher than for solid wire.

What this doesn't tell you

It doesn't give a current rating (ampacity). How much current a wire can carry without overheating depends on the wiring code where you are, the insulation's temperature rating, whether it's in a wall, conduit, buried or in free air, how many cables run together and the room temperature. Check your local rules or ask a qualified electrician, and use the voltage drop calculator to see how much a long run loses.