Wire Gauge Calculator
Convert AWG to diameter, cross-section and resistance per metre, with metric equivalents and reference ampacity figures.
How to use this calculator
- 1Enter an AWG number, or a cross-section in mm² to find the nearest gauge.
- 2Choose copper or aluminium.
- 3Add a run length and current to see voltage drop and power lost as heat.
How the calculation works
diameter (in) = 0.005 × 92^((36 − n) ÷ 39) area = π(d/2)² R = ρL ÷ A loop drop = 2 × R × I- n
- AWG number. 0 means 1/0, −1 means 2/0, −2 means 3/0, −3 means 4/0
- 0.005 and 92
- The defining constants: AWG 36 is 0.005 in, and 92 is the ratio spanning the 39 steps to 4/0
- ρ
- Resistivity — 1.724 × 10⁻⁸ Ω·m for annealed copper at 20 °C
- 2 × R × I
- Voltage drop over a circuit, doubled because current flows out and returns
AWG is an exact geometric series, not a lookup table. Every published diameter can be computed from the formula, which is why this calculator derives them rather than embedding figures that could be mistyped.
The scale runs backwards because it originally counted how many times a wire was drawn through progressively smaller dies. More draws meant thinner wire and a higher number.
Three gauge steps roughly double or halve the cross-sectional area, since 92^(3/39) ≈ 1.26 in diameter and squaring that gives about 1.59 — near enough that the rule of thumb holds.
Voltage drop uses twice the run length. Forgetting the return conductor halves the calculated drop and is the most common error in cable sizing.
Worked example
AWG 12 copper on a 10 metre run
- 1.Diameter: 0.005 × 92^((36 − 12) ÷ 39) = 0.005 × 92^0.6154 = 0.0808 in = 2.053 mm.
- 2.Cross-section: π × (2.053 ÷ 2)² = 3.309 mm².
- 3.Resistance per metre: 1.724 × 10⁻⁸ ÷ (3.309 × 10⁻⁶) = 5.21 mΩ/m.
- 4.Loop resistance over 10 m: 5.21 × 10 × 2 = 0.1042 Ω — doubled for the return path.
- 5.Voltage drop at 15 A: 0.1042 × 15 = 1.563 V, which is 0.68% of 230 V.
- 6.Power lost as heat: 1.563 × 15 = 23.4 W.
Result: 3.309 mm², 1.56 V drop
Finding the gauge nearest 2.5 mm²
- 1.A 2.5 mm² conductor has diameter 2√(2.5 ÷ π) = 1.784 mm = 0.0702 in.
- 2.Inverting the series: n = 36 − 39 × ln(0.0702 ÷ 0.005) ÷ ln(92).
- 3.ln(14.05) = 2.6425, and ln(92) = 4.5218.
- 4.n = 36 − 39 × 0.5844 = 36 − 22.79 = 13.21.
- 5.So 2.5 mm² sits between AWG 13 and 14, closest to 13 — which is why 2.5 mm² is usually quoted as "roughly AWG 14" in trade tables, erring towards the thinner standard size.
Result: AWG 13.21 — between 13 and 14
Why the numbers run backwards
AWG numbering is inverted — 30 is hair-thin and 4/0 is thicker than a thumb — and the reason is historical rather than arbitrary. The gauge counted how many times a wire had been pulled through progressively smaller drawing dies. More passes meant thinner wire, so a higher number meant less metal.
The scale was later formalised as an exact geometric progression: gauge 36 is 0.005 inches, gauge 4/0 is 0.46 inches, and there are 39 steps between them. Every intermediate diameter follows from that, which is why the published tables can be reproduced exactly by formula.
Two consequences of the geometry are worth carrying around. Three gauge steps roughly double the cross-sectional area, and ten gauge steps multiply it by about ten. Both are close enough to be useful mental arithmetic when sizing a cable.
Voltage drop, and the return conductor everyone forgets
Current has to get back. A 10 metre run means 20 metres of conductor, and calculating drop over the one-way distance halves the answer — the single most common mistake in cable sizing.
The consequences are practical rather than theoretical. Excessive drop dims lights, makes motors run hot and start badly, and wastes energy as heat in the wall. Most guidance caps branch-circuit drop at around 3%, with 5% total from the supply.
Long runs are where it bites, and the fix is counterintuitive: raising the voltage helps far more than thickening the wire. Delivering the same power at twice the voltage halves the current, and since drop is proportional to current while power loss goes with current squared, the loss falls to a quarter. That is the entire argument for high-voltage transmission.
What this assumes, and where it stops
Assumptions
- Solid round conductors. Stranded wire of the same nominal gauge has slightly more resistance, because the strands are longer than the cable.
- Resistivity at 20 °C. Copper resistance rises about 0.4% per °C, so a hot conductor has meaningfully more.
- Voltage drop uses twice the run length, for the outward and return conductors.
Limitations
- Ampacity figures are reference values only. Real allowable current depends on insulation rating, ambient temperature, bundling, installation method and local code — this cannot tell you what is legal to install.
- Assumes DC or low-frequency AC. Skin effect increases effective resistance at high frequencies, particularly in thick conductors.
- Solid conductor geometry only. Stranded cable has a slightly smaller effective copper area for the same nominal size.
- Does not account for temperature rise under load, which raises resistance and therefore drop.
- Not a substitute for a qualified electrician or for the applicable wiring regulations.
Common questions
What is AWG and why do lower numbers mean thicker wire?
American Wire Gauge is a standard sizing scale for round conductors. The numbering is inverted because it originally counted drawing operations — each pass through a smaller die made the wire thinner and increased the number. It is an exact geometric series: diameter = 0.005 × 92^((36 − n) ÷ 39) inches.
How do I convert AWG to mm²?
Compute the diameter from the AWG formula, convert to millimetres, then take π(d/2)². AWG 12 gives 2.053 mm diameter and 3.309 mm². Note that metric cable comes in preferred sizes like 2.5 and 4 mm², so there is rarely an exact match — 2.5 mm² sits between AWG 13 and 14.
How much voltage drop is acceptable?
Around 3% for a branch circuit and 5% total from the supply is the usual guidance. Remember to calculate over twice the run length, since current flows out and back — using the one-way distance halves the result and is the most common sizing error.
How many gauge steps double the wire size?
Three. Going down three AWG numbers roughly doubles the cross-sectional area, and going down ten multiplies it by about ten. Both follow from the geometric series and are accurate enough for quick mental checks.
Sources
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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