How to Calculate Voltage Drop in a Wire Run

Wire has a little resistance, so some of the voltage is used up pushing the current along it. Over a long run, that voltage drop can leave a motor or heater short of voltage. A common guideline is no more than 3% on a branch circuit.

For learning and checking coursework only. Electrical work can kill. Follow the electrical code where you live and have a licensed electrician do or inspect real wiring.

Try it with your own problem ↓

The steps

Find the wire’s resistance per 1,000 ft in a table (in the US, the NEC, Chapter 9, Table 8). 10 AWG copper is 1.24 Ω per 1,000 ft.
For single-phase, double the one-way length: the current goes out on one wire and comes back on the other.
Wire resistance = Ω per 1,000 ft × total wire length ÷ 1,000.
Voltage drop = current × wire resistance (Ohm’s law).
Percent drop = drop ÷ supply voltage × 100. Compare it with the 3% guideline.

A worked example

A 240 V circuit runs 150 ft (one way) in 10 AWG copper and carries 20 A. Find the voltage drop and the percent drop.

10 AWG copper: 1.24 Ω per 1,000 ft.
Wire length, out and back: 2 × 150 = 300 ft.
Wire resistance: 1.24 × 300 ÷ 1,000 = 0.372 Ω.
Voltage drop: 20 A × 0.372 Ω = 7.44 V.
Percent: 7.44 ÷ 240 × 100 = 3.1%. The load gets 240 − 7.44 = 232.56 V.

The drop is 7.44 V, or 3.1%: just over the 3% guideline, so the usual choice would be the next size up (8 AWG).

Why it works

The wire is just a long, thin resistor in series with the load. The current that runs the load also flows through the wire, out and back, and by Ohm’s law that current times the wire’s resistance is the voltage lost on the way. A longer wire, more current or a thinner wire all mean more drop.

Try it with your own problem

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Common mistakes

Forgetting the return wire. Using 150 ft instead of 300 ft halves the answer.
Thinking a bigger AWG number is a bigger wire. It is the other way round: 8 AWG is thicker than 10 AWG.
Using copper values for aluminum. Aluminum has about 1.6 times the resistance of copper of the same size.
Sizing for voltage drop only. The wire must also be rated for the current (its ampacity) under the code.

Questions people ask

What is the circular-mil formula?

VD = 2 × K × I × L ÷ circular mils, with K ≈ 12.9 for copper. For this run: 2 × 12.9 × 20 × 150 ÷ 10,380 ≈ 7.46 V, almost the same.

What is the drop for 12 AWG copper, 100 ft, 16 A at 120 V?

1.98 × 200 ÷ 1,000 = 0.396 Ω, and 16 × 0.396 = 6.336 V, which is 5.28% of 120 V.

Is three-phase different?

Yes: use √3 (about 1.732) in place of the 2.

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