AWG to mm² Calculator converts wire gauge to square millimeters with conductor diameter, circular mil area, resistance, and nearest metric size for faster electrical sizing checks.
How an AWG to mm² Conversion Actually Works
American Wire Gauge and metric cross-sectional area are two unrelated numbering systems, so there’s no shortcut multiplication between them. AWG is defined by ASTM B258, the standard that fixes wire diameter at two reference points — 36 AWG at 0.005 inches and 0000 (4/0) AWG at 0.46 inches — and spaces every size between them along a geometric progression with a common ratio equal to the 39th root of 92.
For any AWG number $n$, diameter in millimeters is:
$$d_n = 0.127 \times 92^{\frac{36-n}{39}}\ \text{mm}$$
Cross-sectional area follows directly from that diameter, using the ordinary area of a circle:
$$A = \frac{\pi}{4} \times d_n^2\ \text{mm}^2$$
The tool also reports diameter in inches (dividing the millimeter figure by 25.4) and in circular mils — the North American unit where area equals the square of the diameter in mils, with no $\pi$ term, since a circular mil is itself defined as the area of a 1-mil-diameter circle rather than measured against one.
Resistance is calculated separately from geometry. At 20°C, resistivity is 17.24 Ω·mm²/km for annealed copper and 28.2 Ω·mm²/km for aluminum — standard reference values for 100% IACS copper and roughly 61% IACS aluminum.
Dividing resistivity by cross-sectional area gives resistance per kilometer at 20°C. Resistance at any other temperature applies the linear temperature-coefficient formula:
$$R_T = R_{20} \times [1 + \alpha (T – 20)]$$
where $\alpha$ is 0.00393 per °C for copper and 0.00403 per °C for aluminum, both referenced to 20°C.
Mass per kilometer comes from that same cross-sectional area, treated as bare-conductor volume — 1 mm² of cross-section over 1 km of length works out to exactly 1 liter of metal — multiplied by density: 8.96 kg/L for copper, 2.70 kg/L for aluminum.
Finally, the calculated area is compared against the standard metric cable sizes used almost everywhere outside North America — the same preferred sizes IEC 60228 defines from 0.5 mm² upward, extended down with the finer increments used for instrument and appliance wiring. The result is an exact match where one exists, or the nearest metric size below and the next one above.
| Property (at 20°C reference) | Copper | Aluminum |
|---|---|---|
| Resistivity | 17.24 Ω·mm²/km | 28.2 Ω·mm²/km |
| Temperature coefficient (α) | 0.00393 /°C | 0.00403 /°C |
| Density | 8.96 kg/L | 2.70 kg/L |
Worked Example: 12 AWG Copper at 75°C
Take a 12 AWG copper conductor running at 75°C — a realistic operating temperature for THHN/THWN-2 insulated wire under load, well above the standard’s 20°C reference point.
Diameter first:
$$d_{12} = 0.127 \times 92^{\frac{36-12}{39}} = 0.127 \times 92^{0.6154} \approx 2.0525\ \text{mm}$$
That’s 0.0808 inches, or 6,529.95 circular mils.
Area:
$$A = \frac{\pi}{4} \times (2.0525)^2 \approx 3.31\ \text{mm}^2$$
Resistance at the 20°C reference is 17.24 ÷ 3.31 ≈ 5.2104 Ω/km. Correcting for 75°C:
$$R_{75} = 5.2104 \times [1 + 0.00393 \times (75-20)] = 5.2104 \times 1.21615 \approx 6.3366\ \text{Ω/km}$$
That’s a 21.62% increase in resistance from the 20°C reference — purely from heat, since the conductor hasn’t changed size or material.
Against the standard metric series, 3.31 mm² falls between 2.5 mm² and 4 mm², with no exact match. The next metric size up, 4 mm², carries about 20.89% more copper than this AWG size actually has.
For a kilometer of this bare conductor: 3.3088 liters of copper, weighing 29.65 kg, or about 290.73 N.
What the Numbers Actually Tell You
The headline mm² figure is a direct geometric conversion — not an ampacity rating and not a recommendation, just the physical cross-sectional area that AWG size occupies. Circular mils is the same area expressed in the unit most North American wire tables use instead, and the two will always track each other exactly for a given AWG size.
An exact match to a standard metric size is rare — AWG and metric cable sizing are two unrelated numbering systems, so most conversions land between two metric sizes rather than on one.
When you’re specifying a metric-labeled cable to replace an AWG-specified conductor, rounding down to the smaller metric size gives you less copper than the AWG size actually has; rounding up to the next size is the safer substitution.
Ω/km values are raw material resistance, not a voltage-drop or line-loss calculation on their own — you’d still need the actual run length and current to turn these figures into a usable number.
What they do show clearly is how much heat matters: at 75°C, this conductor already carries 21.62% more resistance than the same wire measured at the 20°C laboratory reference.
Mass and weight are for bare conductor metal only. Insulation, jacket material, and any armor add to the real weight of finished cable, so these figures will always come in under a manufacturer’s cable weight spec.
What Changes the Result
Because AWG spacing is geometric rather than linear, area doesn’t shrink evenly as the gauge number climbs. Every 3-gauge decrease roughly doubles cross-sectional area, and every 6-gauge decrease roughly doubles diameter — a direct consequence of the 92^(1/39) ratio built into the formula.
Material swaps everything downstream of geometry, even at identical gauge and temperature. Aluminum’s resistivity (28.2 Ω·mm²/km) is roughly 1.6× copper’s (17.24), and its temperature coefficient runs slightly higher too. But aluminum’s density is less than a third of copper’s, so a 12 AWG aluminum conductor at 75°C works out to roughly 10.41 Ω/km resistance and 8.93 kg/km mass — noticeably higher resistance, but far lighter, than the copper figures above.
Every degree above the 20°C reference adds about 0.39% to copper resistance and 0.40% to aluminum resistance. The calculator accepts any input from -50°C to 200°C, but the physical result only makes practical sense within realistic conductor operating temperatures.
AWG sizes run from 4/0 (the largest size this tool supports) down to 40 AWG (the finest), and material is limited to copper or aluminum — there’s no in-between value for either input.
FAQs
What is 12 AWG wire in mm²?
A 12 AWG conductor has a cross-sectional area of about 3.31 mm². That figure comes straight from the AWG diameter formula in ASTM B258 and doesn’t change between copper and aluminum — the conversion is pure geometry.
What’s the difference between AWG and mm² wire sizing?
AWG is a North American logarithmic gauge system where the number gets smaller as the wire gets thicker; mm² is the metric cross-sectional area used almost everywhere else. There’s no simple multiplication between them — converting requires the AWG diameter formula first, then the ordinary area-of-a-circle calculation.
Why doesn’t my AWG size convert to a round metric number?
Because AWG and the standard metric cable sizes are two independent numbering systems that were never designed to align. Most AWG-to-mm² conversions land between two standard metric sizes rather than matching one exactly.
Does wire resistance really change with temperature, or is that just theoretical?
It’s a real, measurable effect, not a rounding artifact. Resistance rises linearly above the 20°C reference point, at roughly 0.39% per °C for copper and 0.40% per °C for aluminum, so a conductor running hot under load has meaningfully more resistance than its rated 20°C value.
Is aluminum wire actually lighter than copper for the same gauge?
Yes, substantially. At the same AWG size, aluminum’s density is less than a third of copper’s, so while aluminum carries noticeably higher resistance at any given gauge, it’s also far lighter per kilometer of run.
What temperature should I use for the resistance calculation?
20°C is the standard reference point the resistivity constants themselves are defined at. For resistance closer to real operating conditions, use the conductor’s expected operating temperature under load, which commonly runs well above 20°C depending on insulation type and ambient conditions.
Can I use this calculator to size a wire for a circuit?
No — this tool converts AWG to metric cross-sectional area and calculates the underlying physical properties. It doesn’t determine ampacity, account for insulation temperature rating, conduit fill, or ambient derating. Circuit sizing needs an ampacity table and, ultimately, a licensed electrician’s sign-off.
What AWG sizes does this calculator cover?
4/0 (0000) AWG down to 40 AWG — from about 107 mm² at the largest end to about 0.005 mm² at the smallest.
These figures are for planning and estimation, not a substitute for code compliance. Final wire sizing, breaker selection, and installation should be verified against the National Electrical Code and any applicable local amendments, and the work performed or inspected by a licensed electrician.