Voltage drop calculator

How the number is worked out

Voltage drop along a run is the current multiplied by the length multiplied by the effective impedance per metre, and then by a factor that depends on the system:

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

The resistance per metre is not a looked-up figure. It 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 is derived from the series definition, d = 0.005 × 92^((36−n)/39) inches, rather than from a table.

A worked example

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

Four things that move the answer more than people expect

• Conductor temperature. Copper resistance rises about 0.39 % per kelvin. A conductor running at 70 °C has roughly 20 % more resistance than the same conductor at 20 °C, so a calculation done at room temperature understates the drop by about a fifth. This is the single most common reason a hand calculation and a measured value disagree.
• Stranding. A stranded conductor is slightly longer than the cable it sits in, because the strands spiral. The factor used here is 1.02, which is the usual approximation for ordinary stranded constructions.
• Reactance. Negligible on small conductors and increasingly significant above roughly 35 mm², where it can dominate. The field is explicit rather than hidden, and it is left at zero unless you supply a value, because the right value depends on the cable construction and spacing.
• Power factor. Only the in-phase component of the impedance contributes to the drop at unity power factor. As the power factor falls, the reactive part starts to matter, which is why the two are combined as R′cosφ + X′sinφ rather than by magnitude alone.

What the permitted limit is

That depends on your jurisdiction, on the type of circuit, and on the edition of the wiring rules in force where you are working, and it is not something this page will tell you. Look it up in your own current copy. The calculator takes whatever limit you give it and reports the percentage it actually achieved, so you can compare the two yourself.

What this page does not calculate

Current carrying capacity, and the corrections for grouping, ambient temperature and installation method that go with it. Those figures are published in national wiring rules under copyright, and they are not reproduced here. Voltage drop is one of several constraints on a conductor size, and satisfying it says nothing about whether the conductor can carry the current safely.

That is what the app is for. It holds each code as a licensed, versioned pack, checks the conductor against every constraint at once, names the one that decided the answer, and keeps the sheet with the job. See what it does.