Voltage drop calculator
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Result
Resistive drop only: the cable reactance is ignored and the power factor is taken as 1, which is accurate for small cross-sections. For large cables (roughly above 25 mm²) the reactance adds noticeably.
Work out the voltage drop along a cable from its material, cross-section, length and current. Choose DC or single-phase AC (two conductors) or three-phase AC, copper or aluminium, and the conductor temperature. The calculator gives the drop in volts and as a percentage, the voltage at the load and the power lost in the cable. It uses the resistance of the conductors only; the cable reactance is ignored, which the note explains.
Step-by-step solution
Resistivity
Resistance of one conductor
Voltage drop
Power lost in the cable
Key formulas
- Conductor resistance
- R = ρ·L/A
- DC or single phase
- ΔV = 2·I·R
- Three phase
- ΔV = √3·I·R
- Resistivity at temperature
- ρT = ρ20·(1 + α·(T − 20 °C))
- Percent drop
- ΔV/V × 100%
How to calculate voltage drop in a cable
- Find the resistivity of the conductor: about 0.0172 Ω·mm²/m for copper and 0.0283 Ω·mm²/m for aluminium at 20 °C, roughly 20% more at 70 °C.
- Resistance of one conductor: R = ρ × L / A, with L the one-way length in metres and A the cross-section in mm².
- DC and single-phase: the current flows out and back, so ΔV = 2 × I × R.
- Three-phase (line-to-line voltage): ΔV = √3 × I × R for a balanced load.
- Divide by the supply voltage for the percentage, and compare it with the limit given in the exercise (for example 3% or 5%).
Questions and answers
What voltage drop is acceptable?
Limits depend on the standard and the country. IEC 60364-5-52 (Annex G) recommends at most 3% for lighting and 5% for other uses in installations supplied from the public network; the US NEC suggests 3% for a branch circuit and 5% in total.
Why is the length one way?
Enter the distance from the supply to the load. The calculator takes care of the return conductor: the factor 2 for two-wire circuits and √3 for three-phase circuits.
Why does temperature matter?
The resistance of copper and aluminium rises by about 0.4% per °C. A PVC-insulated cable at full load runs at about 70 °C, which gives roughly 20% more resistance and voltage drop than at 20 °C.
When is ignoring the reactance not acceptable?
For large cross-sections, roughly 25 mm² and above, the inductive reactance becomes comparable to the resistance, and at a low power factor the drop is then noticeably different. Use the full formula ΔV = √3·I·L·(R cos φ + X sin φ) with the manufacturer’s data.
How is the AWG size converted to mm²?
The diameter is 0.127 mm × 92^((36 − n)/39) for gauge n, with 1/0 to 4/0 counting as 0 to −3. AWG 12 is 3.31 mm² and AWG 10 is 5.26 mm².
Practise it yourself
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