Voltage drop

3 percent rulewire sizinglong runconductor sizingpercent voltage drop

Single-phase and three-phase voltage drop, percent drop and conductor resistance at temperature — sizing a conductor for a long run.

Voltage Drop, Single Phase

V_{d} = \frac{2 \rho L I}{A}

Voltage lost in a single-phase run from conductor resistivity, one-way length, current and area — the 2 counts both conductors.

Voltage Drop, Three Phase

V_{d} = \frac{\sqrt{3} \, \rho L I}{A}

Line-to-line voltage drop on a balanced three-phase run, using √3 rather than 2 because there is no return conductor.

Percent Voltage Drop

\%V_{d} = \frac{100 \, V_{d}}{V_{s}}

Voltage drop expressed as a percentage of the supply voltage, the form codes use for the 3% branch and 5% total limits.

Conductor Resistance Temperature Correction

R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]

Corrects a conductor's resistance from one temperature to another using the material's temperature coefficient of resistance.

How they fit together

Voltage drop is Ohm's law over the length of the run, and the only subtlety is the multiplier. Single phase uses 2 because the current goes out and comes back on two conductors. Three phase uses √3, not 2 and not 3, because the three currents are 120° apart and partially cancel in the return path. Percent drop is the same number expressed against the nominal system voltage, which is how the codes state their limits.

The 3% branch circuit and 5% total figures in the NEC are recommendations in an informational note, not enforceable requirements — but they are what specifications call for and what protects the equipment, since a motor at 10% low voltage draws roughly 10% more current and runs markedly hotter. Size on the actual load current and the actual one-way length, then check the answer against ampacity, because on long runs voltage drop usually governs and you will be upsizing beyond what the breaker needs. The correction most often skipped is temperature: copper resistance rises about 0.393% per °C, so a conductor at 75 °C in a loaded conduit has roughly 20% more resistance than the 20 °C table value — which turns a calculated 2.6% drop into a real 3.1% on exactly the run where it mattered.