Voltage Drop, Single Phase

Also known as single phase VD · wire size voltage drop

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

V_d =

ρ =

L =

I =

A =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

Every conductor is a resistor, and Ohm's law does the rest: the current travels out and back, so the drop is 2 × ρL/A × I. Work in SI and no mystery constant is needed — copper is about 1.72 × 10⁻⁸ Ω·m (1.72 μΩ·cm) at 20 °C, aluminium about 2.82 × 10⁻⁸. Feeding a 20 A load 50 m away on 4 mm² copper drops 2 × 1.72e−8 × 50 × 20 / 4e−6 = 8.6 V, unacceptable on a 230 V circuit and a clear call for larger cable.

North American practice hides the same physics in the constant K in V_d = 2KIL/cmil, where K ≈ 12.9 Ω·cmil/ft for copper and 21.2 for aluminium — those numbers are just ρ expressed in circular-mil-feet. Two traps: use the one-way run length (the 2 is already there), and remember K rises with temperature, which is why 12.9 is a 75 °C figure while cold-copper calculations use about 10.4.

Voltage Drop, Single Phase

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

Where

$V_{d}$ = Voltage drop
$\rho$ = Conductor resistivity
$L$ = One-way run length
$I$ = Load current
$A$ = Conductor area

Missing one of these? Work it out first, then come back

Voltage drop — Percent Voltage Drop, Voltage Drop, Three Phase
Conductor resistivity — Voltage Drop, Three Phase, Resistance of a Wire (R = ρL/A)
One-way run length — Voltage Drop, Three Phase, Motional EMF (ε = BLv)
Load current — Three-Phase Motor Full-Load Current, Current Divider
Conductor area — Voltage Drop, Three Phase, Magnetic Flux (Φ = BA cos θ)

Part of this formula set

Voltage drop

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