What this calculator does
Look up how thick a wire gauge really is, or find the gauge of a wire you've measured. American Wire Gauge (AWG) is the sizing system for electrical wire in North America. Its numbers run backwards: a larger gauge number means a thinner wire. So 22 AWG is hookup wire for electronics, while 4/0 (written 0000) is a heavy service cable. The sizes aren't random. They follow a set formula, and this calculator uses it to convert between gauge, diameter, area and resistance.
Start from a gauge to see its diameter in millimeters and inches. You'll also get its cross-sectional area (the size of the cut end) in mm² and kcmil. And you'll see its resistance per kilometer and per 1000 feet, in copper or aluminum. Or start from a measured diameter or a metric cable area. Then you'll get the exact in-between gauge number and the nearest standard size. A full table from 0000 to 40 AWG is shown below the results.
Where it's used
Why this math matters outside the classroom:
- Household circuits. Electricians commonly use 12 AWG copper for 20 A household circuits and 14 AWG for 15 A ones, in line with US wiring codes.
- Rule of three. Every 3 steps down in gauge number roughly doubles a wire's cross-sectional area.
- Speaker wire. Audio installers choose thicker speaker wire for long runs so less power is lost in the cable.
- Jewelry making. Jewelry makers match wire to bead holes, knowing that 20 AWG is about 0.81 mm across.
- Unlabeled wire. Hobbyists measure a bare conductor with calipers and look up the nearest gauge to identify unlabeled wire.
How to use it
- Choose whether you're starting from an AWG gauge, a diameter or an area.
- Pick the gauge from the list. Or enter the diameter (mm or inches) or area (mm² or kcmil) of the bare metal wire.
- Choose copper or aluminum for the resistance figures.
- Read the results, and use the table to compare neighboring sizes.
What the inputs mean
- Wire gauge
- The "aught" sizes are written several ways: 0000 = 4/0, 000 = 3/0, 00 = 2/0, and 0 = 1/0. In the formula they count as −3, −2, −1 and 0.
- Conductor diameter
- Measure the bare metal, not the insulation. Stranded wire is a little wider overall than a solid wire of the same gauge, because of the gaps between strands. So measuring stranded wire tends to read one size thick.
- Cross-sectional area
- Metric cable is sold by area (for example 1.5, 2.5, 4 or 6 mm²). Large North American wires are sold in kcmil (thousands of circular mils), such as 250 or 500 kcmil.
Formula and method
d = 0.127 mm × 92^((36 − n) ÷ 39) n = 36 − 39 × ln(d ÷ 0.127 mm) ÷ ln(92) A = π ÷ 4 × d² kcmil = (d in mils)² ÷ 1000, 1 mil = 0.001 in R per length = ρ ÷ A ρ(copper) = 1.724e-8 Ω·m, ρ(aluminum) = 2.82e-8 Ω·m (at 20 °C)
In these formulas, n is the gauge number and d is the diameter. A is the cross-sectional area and R is the resistance. ρ (rho) is the resistivity, how strongly the metal resists current. ln is the natural logarithm, which undoes the power in the first formula. Ω (ohm) is the unit of resistance, and 1.724e-8 means 1.724 × 10⁻⁸.
AWG is set by two fixed points. 36 AWG is 0.005 in (0.127 mm) across, and 0000 AWG is 0.46 in. There are 39 gauge steps between them. Each step shrinks the diameter by the same ratio, the 39th root of 92, about 1.123. As a result, every 6 gauges roughly halves the diameter. Every 3 gauges roughly halves the area and doubles the resistance.
A circular mil is the area of a circle one mil (a thousandth of an inch) across. So a wire's area in circular mils is its diameter in mils, squared. Dividing by 1000 gives kcmil. Resistance per length is resistivity divided by area. The calculator uses standard 20 °C values for annealed copper and electrical-grade aluminum.
Worked example
What are the dimensions and resistance of 10 AWG copper wire?
- Diameter: d = 0.127 × 92^((36 − 10) ÷ 39) = 2.588186728 mm, which is 0.10190 in.
- Area: A = π ÷ 4 × 2.588186728² = 5.2611549545 mm², or about 10.383 kcmil.
- Resistance: 0.01724 × 1000 ÷ 5.2611549545 = 3.27684703 Ω/km, about 0.9988 Ω per 1000 ft.
Result: 10 AWG is about 2.588 mm across, with an area of 5.261 mm² and roughly 1 Ω of resistance per 1000 ft of copper.
Understanding the result
The nearest-gauge result rounds to the closest point on the AWG scale. If a measured wire falls halfway between two sizes, measure again more carefully. Remember that insulation and stranding make wire look thicker.
Metric and AWG sizes don't line up exactly. For example, 2.5 mm² sits between 14 AWG (2.08 mm²) and 12 AWG (3.31 mm²). When you swap one for the other in a real installation, never choose the smaller area.
Resistance figures help you estimate voltage drop and power loss. They are not ampacity ratings. How much current a wire may safely carry depends on its insulation, how it's installed and code rules.
Assumptions and limitations
- Sizes are for solid, round wires worked out from the AWG formula, which matches standard tables to within rounding.
- Resistance is DC resistance at 20 °C.
- Sizes larger than 0000 are given in kcmil, not AWG.
- Stranded wires are slightly wider overall, with slightly higher resistance, than solid wire of the same gauge.
- Resistance rises with temperature (about 0.4% per °C for copper). For AC, it also rises with frequency, because of the skin effect (current crowding toward the wire's surface).
- This is a sizing reference, not an ampacity or code check. Wire for real installations must be chosen according to your local electrical code, and a licensed electrician should confirm it.
Frequently asked questions
Why do bigger AWG numbers mean thinner wire?
The gauge number first counted how many times wire was pulled through smaller and smaller dies (shaped holes). More pulling steps made thinner wire, so the number grew as the wire shrank.
What does 4/0 mean?
It's the same as 0000 AWG, four steps thicker than 0 AWG and about 11.68 mm (0.46 in) across. 3/0, 2/0 and 1/0 are 000, 00 and 0. Beyond 4/0, sizes are given in kcmil, such as 250 kcmil.
How do I convert mm² to AWG?
Choose Area and enter the mm² value. The calculator finds the diameter, the exact gauge number and the nearest standard gauge. For example, 4 mm² works out to gauge 11.18, nearest 11 AWG.
How much does the resistance change between gauges?
Each gauge step changes the area by about 26%, so resistance changes by the same factor. Three steps nearly double it. 10 AWG copper is about 1 Ω per 1000 ft, and 13 AWG about 2 Ω.
How this calculator is checked
Method: AWG definition d = 0.127 mm × 92^((36 − n)/39); circular-mil area; R = ρ/A with ρ = 1.724e-8 Ω·m (copper) and 2.82e-8 Ω·m (aluminum) at 20 °C. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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