What American Wire Gauge actually is
AWG is a geometric progression, not a list. Two diameters are fixed by definition: 4/0 is 0.4600 inches and 36 AWG is 0.0050 inches. Between them lie 39 equal ratio steps, so each gauge number is 92^(1/39) = 1.1229 times the diameter of the next smaller number. Everything else — area, circular mils, resistance — follows from that one relation, which is why a formula reproduces the whole table exactly rather than approximating it.
The counting runs backwards, which is the first thing that confuses newcomers. Larger gauge numbers mean thinner wire. Past 1 AWG the numbering would have to go to zero and below, so the sizes are written 1/0, 2/0, 3/0 and 4/0 (spoken “one aught” through “four aught”) and correspond to n = 0, −1, −2 and −3 in the formula. Above 4/0 the gauge is abandoned entirely and conductors are specified in thousands of circular mils — 250 kcmil, 500 kcmil, 1000 kcmil.
The historic reason for the ratios is drawing dies. Wire was pulled through successively smaller dies, and the gauge number originally counted how many drawing operations the wire had been through, which is why a bigger number means a thinner wire. The modern definition keeps the progression and discards the process.
Two consequences are worth memorising. Three gauge numbers change the area by 92^(6/39) = 2.0050, so three sizes doubles or halves the area. Six gauge numbers change the diameter by the same factor, so six sizes doubles or halves the diameter. Ten sizes changes the area by a factor of 10.16, near enough that going ten gauges thinner cuts the copper by an order of magnitude and multiplies resistance by ten.
Circular mils, kcmil and why North America uses them
A circular mil is the area of a circle one mil — one thousandth of an inch — in diameter. Its point is that it removes π from the arithmetic: the area of any round conductor in circular mils is simply the square of its diameter in mils. A 0.0808 in conductor is 80.8 mils across, so it is 80.8² = 6,529 circular mils. No multiplication by π/4 is needed, which mattered enormously in the era of slide rules and still makes code tables easy to read.
One circular mil is π/4 square mils, which works out to 5.067 × 10⁻⁴ mm². So 1 kcmil (a thousand circular mils) is 0.5067 mm², and the familiar 500 kcmil feeder is 253.4 mm². Going the other way, 1 mm² is 1,973.5 circular mils. The NEC uses circular mils throughout Chapter 9 and in the grounding-conductor upsizing rule of 250.122(B), where you compare installed circular mils against required circular mils — see the equipment grounding conductor calculator for that calculation.
IEC and most of the world outside North America specify conductors directly in mm², using a preferred series — 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240, 300 — defined in IEC 60228. These do not line up with AWG sizes, which is the practical problem this calculator solves: 16 mm² falls between 6 AWG (13.30 mm²) and 4 AWG (21.15 mm²), so a direct substitution always involves a decision about which way to round.
Round up unless you have a reason not to. A conductor smaller than the one specified is smaller in ampacity, higher in resistance and worse for voltage drop, and none of those errors announces themselves at installation. Where the substitution is for a code-required minimum size, rounding down is simply non-compliant.
Worked example: converting 12 AWG and going back from 16 mm²
Take 12 AWG, the workhorse of 20 A branch circuits in North America.
- Exponent. (36 − 12)/39 = 24/39 = 0.615385.
- Diameter. d = 0.127 × 92^0.615385. Since ln 92 = 4.521789, the exponent is 0.615385 × 4.521789 = 2.782639, and e^2.782639 = 16.1601. So d = 0.127 × 16.1601 = 2.0523 mm.
- In inches. 2.0523 / 25.4 = 0.080800 in, which is the 0.0808 in printed in every wire table.
- Area. A = πd²/4 = 3.141593 × 4.2119 / 4 = 3.3080 mm², normally quoted as 3.31 mm².
- Circular mils. The diameter is 80.80 mils, so cmil = 80.80² = 6,528.6, quoted as 6,530.
- Resistance. R = ρ/A with ρ = 1.7241 × 10⁻⁸ Ω·m. Per kilometre, R = 1.7241 × 10⁻₈ × 1000 / (3.3080 × 10⁻⁶) = 5.2115 Ω/km, which is 1.588 Ω per 1,000 ft.
Now the reverse. A European drawing specifies 16 mm² and you need the American equivalent.
- Diameter from area. d = √(4A/π) = √(4 × 16 / 3.141593) = √20.3718 = 4.5135 mm.
- Gauge number. n = 36 − 39 × ln(4.5135/0.127)/ln 92 = 36 − 39 × ln(35.539)/4.521789 = 36 − 39 × 3.5705/4.521789 = 36 − 39 × 0.78962 = 36 − 30.795 = 5.205.
- Bracket it. 5.205 lies between 6 AWG and 5 AWG, and 5 AWG is not a stocked building-wire size. In practice 16 mm² is replaced by 6 AWG (13.30 mm²) only if the smaller area is acceptable, and by 4 AWG (21.15 mm²) when it is not — the safe substitution is 4 AWG.
Check the direction of that decision against the numbers rather than intuition: 13.30/16 = 0.831, so 6 AWG has 16.9% less metal than the specified conductor, while 4 AWG has 21.15/16 = 1.322, or 32.2% more. Resistance moves inversely, so the 6 AWG substitution raises resistance by 1/0.831 − 1 = 20.3%.
How to use the numbers you get
Use the area for anything about current-carrying capacity and the diameter for anything about physical fit. Ampacity, resistance, voltage drop and grounding-conductor upsizing all scale with area. Conduit fill, bending radius, terminal barrel size and cable gland selection all depend on diameter — and on the overall diameter of the finished cable, which includes insulation and, for stranded conductors, the gaps between strands.
That gap matters more than people expect. A stranded conductor of a given AWG has the same metal area as the solid one by definition, but its circumscribed diameter is larger because the round strands cannot fill a circle completely. A 19-strand 4/0 conductor carries the same 107.2 mm² of copper as solid 4/0, in strands of 11.684/√19 = 2.68 mm each, but its outside diameter is roughly 5–10% greater than solid. Always take the outside diameter from the manufacturer's data for conduit fill, never from this geometric calculation.
Compare materials by area, not by gauge. Aluminium's resistivity of 2.8264 × 10⁻⁸ Ω·m is 1.639 times copper's 1.7241 × 10⁻⁸, so an aluminium conductor of the same size has 63.9% more resistance. Since three AWG sizes double the area, restoring the copper resistance takes 39 × ln(1.639)/ln(92) ÷ 2 ≈ 2.1 gauge sizes, which is why the practical rule is that aluminium runs two sizes larger than copper for a comparable job.
Finally, remember that the resistance here is DC at 20 °C for a solid round conductor. Real conductors run hotter — copper resistance rises about 0.393% per °C — and at power frequencies large conductors show skin effect. NEC Chapter 9 Table 8 quotes copper at 75 °C, which is why its figures are around 20% higher than the ones on this page. For a run-length voltage drop, use the voltage drop calculator, which applies the temperature and AC corrections.
AWG size chart: diameter, area, circular mils and resistance
| AWG | Diameter (in) | Diameter (mm) | Area (mm²) | Circular mils | Ω/km (Cu) |
|---|---|---|---|---|---|
| 4/0 | 0.4600 | 11.6840 | 107.2193 | 211,600 | 0.161 |
| 3/0 | 0.4096 | 10.4049 | 85.0288 | 167,806 | 0.203 |
| 2/0 | 0.3648 | 9.2658 | 67.4309 | 133,077 | 0.256 |
| 1/0 | 0.3249 | 8.2515 | 53.4751 | 105,535 | 0.322 |
| 1 | 0.2893 | 7.3481 | 42.4077 | 83,693 | 0.407 |
| 2 | 0.2576 | 6.5437 | 33.6308 | 66,371 | 0.513 |
| 3 | 0.2294 | 5.8273 | 26.6705 | 52,635 | 0.646 |
| 4 | 0.2043 | 5.1894 | 21.1506 | 41,741 | 0.815 |
| 6 | 0.1620 | 4.1154 | 13.3018 | 26,251 | 1.296 |
| 8 | 0.1285 | 3.2636 | 8.3656 | 16,510 | 2.061 |
| 10 | 0.1019 | 2.5882 | 5.2612 | 10,383 | 3.277 |
| 12 | 0.0808 | 2.0525 | 3.3088 | 6,530 | 5.211 |
| 14 | 0.0641 | 1.6277 | 2.0809 | 4,107 | 8.285 |
| 16 | 0.0508 | 1.2908 | 1.3087 | 2,583 | 13.174 |
| 18 | 0.0403 | 1.0237 | 0.8230 | 1,624 | 20.948 |
| 20 | 0.0320 | 0.8118 | 0.5176 | 1,022 | 33.308 |
| 22 | 0.0253 | 0.6438 | 0.3255 | 642 | 52.962 |
| 24 | 0.0201 | 0.5106 | 0.2047 | 404 | 84.213 |
Every value is computed from the ASTM B258 definition rather than transcribed, so the progression is exact. Published tables round these figures, which is why a handbook may show 6,530 circular mils for 12 AWG where the definition gives 6,528.6.
Conversion traps
- Assuming an AWG size and a metric size are interchangeable because they are close. 16 mm² is not 6 AWG; it is 20% more metal. Substituting the smaller size raises resistance and lowers ampacity, and both effects are invisible until something runs hot.
- Confusing square mils with circular mils. A circular mil is π/4 of a square mil. Treating them as equal makes every area 27% too large.
- Using the conductor diameter for conduit fill. Fill is calculated on the outside diameter of the insulated conductor, from NEC Chapter 9 Table 5, not on the bare metal diameter computed here.
- Assuming a stranded conductor is thinner than a solid one of the same gauge. It has the same metal area and a larger outside diameter, because the strands do not pack perfectly.
- Reading this resistance as the value in the NEC. Chapter 9 Table 8 quotes copper at 75 °C, roughly 20% higher than the 20 °C values here, and gives separate AC resistances in Table 9 for larger sizes where skin effect matters.
- Mixing up the aught sizes. 1/0 is n = 0 and 4/0 is n = −3. Entering 4 for 4/0 gives you 4 AWG, which is a fifth of the area.
- Using AWG for steel or for aluminium building wire without checking the standard. AWG defines geometry only; the applicable conductor standards and code tables differ by material, and steel wire is commonly specified in its own gauge systems.
Key terms
- Mil
- One thousandth of an inch, 0.0254 mm. Wire diameters in North American practice are frequently quoted in mils.
- Circular mil (cmil)
- The area of a circle one mil in diameter. The area of a round conductor in circular mils is the square of its diameter in mils, which removes π from the arithmetic.
- kcmil
- One thousand circular mils, equal to 0.5067 mm². The unit used for North American conductors larger than 4/0.
- IACS
- International Annealed Copper Standard. 100% IACS corresponds to a resistivity of 1.7241 × 10⁻⁸ Ω·m at 20 °C; aluminium conductor grade is about 61% IACS.
AWG, metric sizes and where each is required
Which system you must use is a matter of jurisdiction, not preference. Installations under the NEC specify conductors in AWG and kcmil, and the code's ampacity, fill and grounding tables are all indexed that way. Installations under IEC 60364 and the national wiring rules derived from it specify mm² from the IEC 60228 preferred series. Equipment sold internationally routinely carries terminals marked in both, and the marking is what governs what may be landed there.
The friction shows up in three places. Importing equipment with metric-sized pigtails into a North American panel means finding a listed connector rated for both conductors. Exporting a North American design means restating every conductor in the metric series and re-checking ampacity against the local tables, which use different ambient assumptions and different installation methods. And multinational specifications frequently list both, in which case the two are rarely exactly equal and the drawing should say which one governs.
Do not convert ampacity along with the size. Ampacity is not a property of the metal area alone; it depends on the insulation temperature rating, the installation method, the ambient and the number of grouped conductors, and the NEC and IEC treat all four differently. Convert the geometry here, then run the ampacity calculation in whichever code applies — the ampacity derating calculator covers the NEC path, starting from Table 310.16 and applying the correction and adjustment factors.
Finally, keep circular mils in your toolkit even if you work in millimetres. The NEC's proportional upsizing rules, notably 250.122(B) for equipment grounding conductors, are written in circular mils, and doing that arithmetic in mm² works only if you convert consistently at both ends. The ratio is what matters, and the ratio is the same in either unit.