The formulas
then, for the round trip the current makes:
The resistivities used are ρ = 0.0175 Ω·mm²/m for copper and 0.028 for aluminium (20 °C values). This resistive calculation is accurate for the cable sizes instrumentation and small power work uses; cable reactance only becomes significant above ~50 mm² or at poor power factors.
Worked example
A 25 A three-phase motor, 120 m from the panel, on 4 mm² copper, 415 V system:
- R′ = 0.0175 ÷ 4 = 0.004375 Ω/m (= 4.375 Ω/km)
- Vd = 1.732 × 120 × 25 × 0.004375 = 22.7 V
- Percentage: 22.7 ÷ 415 = 5.5% — fails a 5% criterion; the next size (6 mm²) gives 3.7% ✔
Field notes
- Length is one-way; the formula handles the return. Entering the round-trip length double-counts — the most common misuse of these calculators.
- Temperature raises resistance ~0.4%/°C for copper: a conductor at 70 °C has ~20% more resistance than the 20 °C table value. Size with margin.
- 24 V DC circuits are the sensitive ones: the same absolute drop is ten times the percentage of a 240 V circuit. Long solenoid and instrument power runs deserve this check — and for 4-20 mA loops specifically, use our loop voltage drop calculator, which works in loop-resistance terms.
- Voltage drop and ampacity are separate checks. A cable can pass current safely yet still drop too much voltage over a long run — always check both.
Frequently asked questions
What is the formula for cable voltage drop?
DC and single-phase: Vd = 2 × L × I × R′ (the factor 2 covers both conductors). Balanced three-phase: Vd = √3 × L × I × R′, where L is the one-way run length and R′ the conductor resistance per unit length.
What is an acceptable voltage drop percentage?
Common design limits are 3% for lighting/branch circuits and 5% total from source to load, per typical wiring codes. Motor feeders often target 3% to protect starting torque.
What is the resistance of copper cable per km?
At 20 °C: 1.5 mm² ≈ 12.1 Ω/km, 2.5 mm² ≈ 7.41, 4 mm² ≈ 4.61, 6 mm² ≈ 3.08, 10 mm² ≈ 1.83, 16 mm² ≈ 1.15, 25 mm² ≈ 0.727 (per IEC 60228 Class 1/2 values).
Does voltage drop depend on the supply voltage?
The drop in volts does not — it depends on current, length and resistance. But the PERCENTAGE drop does: the same 6 V drop is 2.5% on a 240 V circuit and 26% on a 24 V DC circuit, which is why low-voltage DC runs are so sensitive.
Provided for reference and education. Cable sizing for installations must follow the applicable wiring code. See our disclaimer.