The American Wire Gauge (AWG) number encodes a wire's thickness: the diameter follows d = 0.127 × 92^((36 − AWG)/39) mm, from which the cross-sectional area and resistance fall out. The scale runs backwards — a lower number is a thicker wire with more copper and less resistance. From the area you get the resistance per length using copper's resistivity, and multiplying by your run length gives the total. It's the quick way to turn a gauge into real diameter, area and ohms.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the AWG diameter formula and copper resistivity 1.724×10⁻⁸ Ω·m.
The wire gauge equations
The diameter formula reproduces the geometric AWG progression — a 6-gauge step changes the diameter by about a factor of two, and a 3-gauge step roughly halves or doubles the area. Squaring the diameter and scaling by π/4 gives the area; dividing copper's resistivity by that area gives the resistance per metre (multiply by 1000 for per km). Multiply by the run length for the total, remembering a circuit's out-and-back loop is twice the one-way length.
Worked example — an AWG 12 run
Scenario: You're using AWG 12 copper wire for a 50-metre run. What are its diameter, area and resistance?
AWG 12 is 2.053 mm across with a 3.31 mm² copper cross-section and about 5.21 Ω/km, so a 50 m run is roughly 0.26 Ω one way — or about 0.52 Ω for the full out-and-back loop. Step up to AWG 10 (3.31 → 5.26 mm², 3.28 Ω/km) and the resistance drops by over a third; drop to AWG 14 and it climbs to 8.28 Ω/km. This is exactly the trade-off behind choosing a heavier gauge to cut voltage drop on long runs.
Frequently Asked Questions
d = 0.127 × 92^((36−n)/39). AWG 12 = 2.053 mm, area 3.31 mm².
≈ 5.21 Ω/km. AWG 10 ≈ 3.28; AWG 14 ≈ 8.28 Ω/km. A 50 m run of AWG 12 ≈ 0.26 Ω.
Yes — the scale is reversed. Smaller number = thicker wire = more area = less resistance.
Ω/km × length(m)/1000. Loop resistance (out + back) is twice the one-way value.
No — ampacity depends on insulation, install and code. This is geometry and resistance only.