How to Calculate Voltage Drop in a Cable

A cable has resistance of its own, so the voltage arriving is lower than the voltage sent. That difference is the voltage drop.

$\rho$ is the resistivity, $L$ the one-way length and $A$ the cross-sectional area of the conductor. The length is doubled because the current runs out along one conductor and back along the other. The resistivity of copper at 20°C is 0.0172 and of aluminium 0.0282, in Ω·mm²/m.

Example

Carry 20 A along 30 m of 5.5 mm² copper. The resistance is $0.0172 \times 60 \div 5.5 = 0.188$ Ω and the drop is $20 \times 0.188 = 3.75$ V, which is 3.75% of a 100 V supply. The cable wastes $20 \times 3.75 = 75$ W, all of it as heat.

Going up a size

Doubling the area halves the resistance, and with it both the drop and the loss. Thicker cable is specified for long runs and heavy currents precisely to hold these down.

Notes

Resistivity changes with temperature. Copper grows more resistive as it warms, so a hot cable drops more than a cold one. Design constants used in wiring regulations build in an allowance for this.

This calculation is for a single-phase two-wire circuit. A three-phase three-wire circuit returns the current differently and carries a smaller factor.