How AWG sizes are defined
American Wire Gauge is a geometric series. 36 AWG is defined as 0.005 in and 0000 (4/0) AWG as 0.46 in, with 39 equal steps between them. Each gauge is 92^(1/39) ≈ 1.123 times the diameter of the next smaller one: d = 0.127 mm × 92^((36 − n) ÷ 39).
A useful rule: every 3 gauges roughly doubles or halves the area, and every 6 gauges doubles or halves the diameter.
SWG and metric sizes
The British Standard Wire Gauge (SWG) is a table of fixed diameters rather than a formula. For example, 14 SWG is 0.080 in (2.032 mm), while 14 AWG is 1.628 mm, so the same number means different sizes in the two systems.
Metric cable is sold by cross-sectional area in mm² (1.5, 2.5, 4, 6 mm² and so on). Area = π ÷ 4 × d².
Resistance
DC resistance per length is resistivity divided by area. Solid copper 12 AWG is about 5.21 Ω/km (1.59 Ω per 1000 ft) at 20 °C. Stranded wire is about 2% higher, and resistance rises with temperature.