Understanding AWG Wire Gauge and Its Formula
Where the AWG scale comes from, why bigger numbers mean thinner wire, and how diameter, area and resistance connect.
A gauge born from the drawing process
American Wire Gauge dates from the era when wire was made by pulling metal through a series of progressively smaller dies. The gauge number counts, in effect, how many drawing steps a wire has been through, which is why a higher number means a thinner conductor. That manufacturing history is captured today by a single geometric formula, diameter equals 0.127 x 92^((36 - AWG) / 39), anchored so that AWG 36 is 0.127 mm and AWG 0000 is 11.684 mm. Because the ratio between consecutive sizes is constant, the whole table is defined by just two reference points.
The 3-step and 6-step rules of thumb
The geometric spacing gives electricians two handy shortcuts. Going up six gauge numbers, say from AWG 12 to AWG 18, roughly halves the diameter, and going down six roughly doubles it. Going up three gauge numbers roughly halves the cross-sectional area, since area scales with the square of diameter. These rules explain why AWG 12 has about 3.309 mm2 of copper while AWG 24, twelve steps thinner, has only about 0.205 mm2, a factor near sixteen. The calculator gives the exact figures, but the rules help you sanity check them in your head.
From area to resistance and voltage drop
Once the area is known, DC resistance follows from R = rho x length / area. Using copper's resistivity of 1.68e-8 ohm-metres and a 1000 m length, the tool reports resistance per kilometre, for example about 5.08 ohm/km for AWG 12 and 82.06 ohm/km for AWG 24. That number is what drives voltage drop over a long run: multiply resistance by length and by current to estimate the volts lost in the cable. Sizing up a gauge or two to cut resistance is often the cheapest fix for a run that sags under load.
Solid copper, temperature and real cable
The figures here assume a solid copper conductor at 20 C, which is the standard reference condition. Stranded wire of the same gauge has a slightly smaller effective copper area because of the gaps between strands, so its resistance is marginally higher. Copper's resistance also rises by roughly 0.4 percent per degree Celsius, so a hot cable carries more resistance than the table shows. Aluminium conductors, common in large feeders, have about 1.6 times the resistivity of copper, so they need a larger area for the same performance.