Voltage drop calculator

How to calculate voltage drop

The drop along a run is the current times the length times the effective impedance per metre, times a factor for the type of system:

k = 2 for a single phase or DC two-wire circuit, because the current goes out and back. k = √3 for a balanced three phase circuit, measured line to line.

Resistance per metre comes from the resistivity of the metal and the cross-sectional area of the conductor:

with ρ₂₀ = 1.7241 × 10⁻⁸ Ω·m and α = 0.00393 /K for copper, and 2.8264 × 10⁻⁸ Ω·m and 0.00403 /K for aluminium. For AWG sizes the area comes from the gauge formula, d = 0.005 × 92^((36−n)/39) inches.

A worked example

Take 32 A on a balanced three phase 400 V circuit: 45 m of 6 mm² copper at 70 °C, power factor 0.9, reactance ignored. At 70 °C the resistivity is 2.063 × 10⁻⁸ Ω·m, so R′ is 0.003507 Ω/m with the stranding factor. The effective impedance at cosφ = 0.9 is 0.003156 Ω/m, and the drop is √3 × 32 × 45 × 0.003156 = 7.87 V, or 1.97 % of 400 V. The sheet above shows each of those steps with its inputs.

Four things that change the answer more than you’d expect

• Conductor temperature. Copper resistance goes up about 0.39 % per degree. At 70 °C a conductor has roughly 20 % more resistance than at 20 °C, so the real drop is about a fifth higher than a room-temperature calculation says. It’s the most common reason a hand calculation doesn’t match what you measure.
• Stranding. The strands spiral, so each one is a little longer than the cable itself. This calculator uses a factor of 1.02, the usual figure for ordinary stranded cable.
• Reactance. Small on small conductors, but it matters more and more above about 35 mm² and can end up larger than the resistance. It stays at zero unless you enter a value, because the right figure depends on how the cable is built and laid.
• Power factor. At unity power factor only resistance counts. As the power factor drops, reactance starts to count too, which is why the formula uses R′cosφ + X′sinφ.

What’s the allowed limit?

It depends on where you work, the type of circuit and the edition of the wiring rules in force there, so check your own copy. This page gives you the percentage, and you compare it with your limit. If you want the smallest size that stays inside a limit, the wire size calculator does that.

What this page doesn’t calculate

Current-carrying capacity, and the corrections for grouping, ambient temperature and installation method that go with it. Those figures are in national wiring rules, which are copyrighted, so they aren’t here. Passing on voltage drop doesn’t tell you whether the cable can carry the current safely.

The app does that part. It checks the cable against every rule at once, tells you which one decided the size, and saves the sheet with the job. See the app.