The selection of an appropriate cable size is a fundamental task in electrical engineering. An undersized cable can overheat, causing insulation failure, fire, or excessive voltage drops that impair equipment performance. An oversized cable, while safe, is economically wasteful, requiring unnecessary capital expenditure on copper or aluminum. Therefore, the formula for cable size calculation is not a single equation but a decision-making framework built upon two primary electrical constraints: current-carrying capacity (ampacity) and voltage drop . The final size is the larger of the two calculated values, often rounded up to a standard manufacturing dimension. 1. The Ampacity or Heating Formula The most critical constraint is thermal. When current ($I$) flows through a conductor of resistance ($R$), heat is generated at a rate of $I^2R$ (Joule's law). The cable must dissipate this heat without exceeding its insulation's maximum permissible temperature. The governing formula is deceptively simple:
$$ V_d = \frac{2 \times L \times I \times (R \cos\phi + X \sin\phi)}{1000} $$ formula for cable size calculation
$$ I_{rated} \ge I_{load} $$
$$ V_d = \frac{2 \times L \times I \times R_{dc}}{1000} \quad \text{(simplified)} $$ The selection of an appropriate cable size is
$$ I_{table} \ge \frac{I_{load}}{k_1 \times k_2 \times k_3 \times \dots} $$ Therefore, the formula for cable size calculation is
A more accurate form for incorporates reactance ($X$):