Physics
Cable voltage drop calculator
Enter voltage, current, length and section: you get the drop in volts and per cent, the power lost in the cable, and the first standard section that comes inside the limit you set.
Why the drop has to be checked
A cable is not an ideal conductor: the current running through it uses up some of the voltage, and less arrives at the load than left the board. The formula is ΔV = k·L·I·(R·cos φ + X·sin φ), with k equal to 2 for single-phase and DC, because the current goes out and comes back, and √3 for three-phase. Wiring rules set a limit — commonly 4% from the origin of the installation to the load — and on a long run that limit is what decides the section.
Temperature is the detail most often skipped. Copper's resistivity rises about 0.4% per degree, so a conductor at 70 °C — the working temperature of a PVC-insulated cable at full load — is nearly 20% more resistive than the same conductor at 20 °C. Calculating at room temperature makes a run look acceptable that is not acceptable at its rated current, and the margin that disappears is exactly the one the limit existed to guarantee.
Reactance cannot be ignored on large sections. Resistance falls in proportion to the section; reactance does not, staying around 0.08 mΩ/m whatever the copper. Past about 120 mm² reactance begins to dominate, and doubling the section no longer halves the drop. From there it is better to split the run or raise the voltage than to thicken the cable.
Common mistakes
- Entering the length there and back. What goes here is the one-way run: the factor of 2 for single-phase and the √3 for three-phase already account for the whole path, and doubling the length doubles the answer for nothing.
- Calculating at 20 °C. Tabulated resistivity is at 20 °C, but a cable in service sits at 70 or 90: using the cold figure understates the drop by about a fifth.
- Using a factor of 2 for three-phase. In three-phase the current does not return through a conductor of its own, and the line-to-line drop is √3 times the one-way figure, not 2 — an error of about 15%, always in the wrong direction.
Frequently asked questions
What is the largest voltage drop allowed?
In most installations the reference is 4% from the origin of the installation to the load. Lighting circuits are often held to 3%, because lamps suffer more than other loads from a low voltage.
How do you find the minimum cable section?
Start from the drop allowed and find the section that meets it, then round up to the next standard size. The cable's current-carrying capacity has to be checked too — it depends on how the cable is installed and on the ambient temperature — and the final section is the larger of the two.
Copper or aluminium?
Aluminium is about 64% more resistive, so for the same drop it needs roughly one and a half times the section. It costs less and weighs less, and it is the usual choice for long distribution runs; copper stays the standard inside buildings.
Why does the drop stop falling past a certain section?
Because resistance falls with section but reactance does not: it stays around 0.08 mΩ/m. Past about 120 mm² the reactive part weighs as much as the resistive one, and thickening the cable achieves less and less. Splitting the run or raising the voltage is the better move.
Does this work for direct current?
Yes: in DC there is no reactance and the path factor is 2, as in single-phase. Just choose direct current as the supply; the power factor then has no effect.
How this calculation works
Resistivity at temperature: ρ(T) = ρ₂₀·(1 + α·(T − 20)), with ρ₂₀ = 0.017241 Ω·mm²/m and α = 0.00393 for copper, ρ₂₀ = 0.028264 and α = 0.00403 for aluminium. Resistance of the run: R = ρ(T)·L/S, with L the one-way length in metres and S the section in mm². Reactance: X ≈ 0.08 mΩ/m·L, zero for direct current. Drop: ΔV = k·I·(R·cos φ + X·sin φ), with k = 2 for single-phase and DC, k = √3 for three-phase. Percentage drop: ΔV/V·100. Power lost: n·I²·R, with n the number of conductors carrying the current — 2 for single-phase and DC, 3 for three-phase. Apparent power: V·I for single-phase and DC, √3·V·I for three-phase. The minimum section is the first of the standard series — 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240, 300, 400, 500, 630 mm² — that meets the limit, so that it is a section you can order.