One formula, not a table
American Wire Gauge is defined by two fixed points and a geometric progression between them. The largest tabulated size, 0000 or 4/0, is 0.4600 inches. Thirty-nine steps down, 36 AWG is 0.0050 inches. Every gauge in between is the previous one multiplied by a constant ratio, which works out as:
diameter in inches = 0.005 × 92(36 − n) / 39
with 0 counted as n = 0, 00 as n = −1, 000 as −2 and 0000 as −3. That is where every number on this page comes from, which is worth knowing because published gauge tables are rounded to four decimal places and occasionally rounded inconsistently between one printing and another. Feed 12 into the formula and it gives 0.0808 inches and 6,530 circular mils, which is what the standard tables say. Feed in 10 and it gives 0.1019 inches and 10,383 circular mils, against a tabulated 10,380 — the difference is rounding in the table, not in the formula.
Two consequences of the geometry are worth committing to memory. Six gauge numbers is a factor of two in diameter, because 926/39 is almost exactly 2. Three gauge numbers is therefore a factor of two in area. So 6 AWG has twice the area of 9 AWG and four times the area of 12 AWG, and you can sanity-check any table against that in your head.
Circular mils, and why the unit exists
A circular mil is the area of a circle one mil — one thousandth of an inch — across. It is defined that way precisely so that the area of a round conductor is the square of its diameter in mils, with no factor of pi anywhere. A 0.0808 inch conductor is 80.8 mils across, so it is 80.8² = 6,530 circular mils, and that is the whole calculation. For stranded conductor the total is just the sum over the strands, which is why the unit survived into modern practice: it makes bundles trivial to add up. Above 1,000 circular mils the kcmil is used, so 250 kcmil means 250,000 circular mils, and cable larger than 4/0 is sized in kcmil rather than by gauge number at all.
AWG and metric sizes do not line up
Metric conductors are specified by nominal cross-section in square millimetres, from a standard series — 0.5, 0.75, 1, 1.5, 2.5, 4, 6, 10, 16, 25 and up. That series was not derived from AWG and does not coincide with it anywhere. The nearest metric size shown with each result is the closest member of that series on a ratio basis, and the word to hold onto is closest, not equal:
| AWG | Area (mm²) | Nearest metric | Metric is |
|---|---|---|---|
| 14 | 2.08 | 2.5 mm² | 20% larger |
| 12 | 3.31 | 4 mm² | 21% larger |
| 10 | 5.26 | 6 mm² | 14% larger |
| 8 | 8.37 | 10 mm² | 19% larger |
| 6 | 13.30 | 16 mm² | 20% larger |
| 4 | 21.15 | 25 mm² | 18% larger |
Notice that the nearest metric size is bigger every time in that range, sometimes by a fifth. Substituting in the other direction — putting AWG conductor where a metric size was specified — therefore means going down in area unless you deliberately step up a gauge. That is a decision for whoever is responsible for the installation, and it is not one this page can make.
What the resistance figure is and is not
The ohms per thousand feet shown is Ohm law applied to a solid round conductor: resistivity times length divided by area, using 1.724 × 10−8 ohm-metres for annealed copper and 2.826 × 10−8 for aluminium at 20 °C, with the standard temperature coefficient applied for the 75 °C figure. It lands within a percent or so of published direct-current resistance tables for solid conductor, and the 75 °C column is around 22% higher than the 20 °C column, which is the whole reason the distinction matters — a conductor warm from carrying current has measurably more resistance than the same conductor cold on a shelf.
Stranded conductor reads higher than the figure here, typically by two or three percent, because each strand takes a helical path longer than the cable itself. Coated strands add a little more. Alternating current at higher frequencies adds skin effect on top of all of it. If the number you need is going into a voltage-drop check, the voltage drop calculator is the tool that handles run length, load and the round trip properly.
What this page will not tell you
It will not tell you what size wire to use. Ampacity — how much current a conductor may carry — is not a property of the metal alone. It depends on the temperature rating of the insulation around it, how many current-carrying conductors are bundled or in the same raceway, the ambient temperature, whether the run is in free air or buried or in conduit, the termination temperature rating at both ends, and the edition of the electrical code adopted by the authority having jurisdiction over the work. Two identical 12 AWG copper conductors in two different installations have two different permitted ampacities, and neither of them comes from a diameter.
Use this to identify what you are holding, to translate a specification between systems, or to check a supplier claim against the defining formula. For the sizing decision itself, the wire size calculator and the circuit load calculator take the installation variables as inputs, and the final call belongs to the person signing off the installation.
Questions people ask
Why does my table say 10 AWG is 10,380 circular mils and this says 10,383?
Both are right, and the difference is where the rounding happens. The published figure is calculated from a diameter that has already been rounded to four decimal places, then rounded again. This page calculates from the defining formula and rounds once at the end. The gap is three parts in ten thousand and has no practical consequence — it only shows up if you compare tables digit by digit.
Should I measure over the insulation?
No — the gauge refers to the conductor only, and insulation thickness varies enormously between types for the same conductor size. Strip a short length and measure the bare metal with calipers. If the conductor is stranded, calipers over the bundle read slightly larger than the equivalent solid diameter, because the strands do not pack perfectly; count the strands and measure one instead if you need to be careful about it.
Is AWG the same as SWG or metric wire gauge?
No. Standard Wire Gauge, the older British system, is a different progression with different diameters, so 16 SWG and 16 AWG are not the same wire. Sheet metal gauges are different again and material-dependent — the sheet metal gauge chart on this site covers those, and they have nothing to do with wire. Anything specified in square millimetres is not a gauge system at all, it is a direct statement of area.
Can I work out the ampacity from the circular mils?
Not legitimately. Rules of thumb of that shape circulate widely and they are all missing the variables that actually govern the answer: insulation temperature rating, bundling, ambient temperature, installation method, termination ratings and the adopted code. The conductor is one input to that calculation and not the dominant one in many installations. Sizing a circuit from a diameter alone is how conductors end up undersized in exactly the conditions where it matters.
What happens above 4/0?
Gauge numbers stop being used and cable is specified directly in thousands of circular mils — 250 kcmil, 350 kcmil, 500 kcmil and so on. The formula still extends mathematically past 4/0, and this page will not follow it there because nobody labels cable that way, so a number it produced would not match anything you could buy or specify.