The relationship between wire gauge and thickness is that wire gauge measures how thick a wire is. However, the relation is inverse, such that a higher gauge number represents a lower diameter.
There are two common gauge systems in use worldwide. First is the American Wire Gauge (AWG) system. This features 40 gauges, namely numbers 0000, 000, 00, 0, then 1 to 36. Wires with gauge No. 0000 have the largest diameter, measuring 0.46 inches (or 12 millimeters), while No. 36 represents the smallest diameter at 0.005 inches (or 0.13 millimeters). Under the AWG system, multiplying each diameter by 0.890526 gives the succeeding lower diameter size.
Secondly, there is the Standard Wire Gauge (SWG). This quotes gauge No. 7/0 as the largest size, measuring 0.5 inches (12.7 millimeters) in diameter, and No. 50 as the smallest at 0.001 inches (0.025 millimeters) diameter. Here, the diameter decreases by 10.557% each gauge.