Wire Gauge

Every wire has resistance. Push current through it and some voltage is lost along the way, turning into heat. In a 12 V system there is not much voltage to spare, so cables are usually sized to limit the drop rather than just to avoid melting.

Resistance of a wire

with resistivity $\rho = 0.0172\ \Omega\,\text{mm}^2/\text{m}$ for copper, length $L$ in metres and cross-section $A$ in mm².

Voltage drop

$k = 2$ when current goes out on one wire and back on another, because it travels the run twice. $k = 1$ if the return is through the body shell, whose resistance is small by comparison.

Minimum cross-section

Rearranged for the area that keeps the drop within a chosen fraction $\delta$ of system voltage $V$:

The sheet then picks the smallest standard gauge that meets both this area and a current rating for bundled chassis wiring. On short runs the current rating is what decides; on long runs voltage drop takes over.

• American Wire Gauge runs backwards: every 3 steps down doubles the area, every 6 steps doubles the diameter.
• Halving the system voltage for the same power doubles the current and halves the allowable drop, so cable area goes up four-fold. That is why 24 V and 48 V systems use so much less copper.