About this calculator
Every cable has resistance, so some voltage is lost along it when current flows. If the drop is too large, motors struggle to start, lamps dim and electronics can reset. This calculator estimates the drop for a DC circuit, a single-phase AC circuit or a balanced three-phase AC circuit, using copper or aluminium conductor data.
Be clear about the length. In a two-wire circuit the current goes out along one conductor and back along the other, so the drop uses twice the one-way route length. If you have already measured the total length of both conductors, choose Total conductor length.
Formula
DC and single-phase: ΔV = 2 × I × L × (R cos φ + X sin φ)
Three-phase (line-to-line): ΔV = √3 × I × L × (R cos φ + X sin φ)
RT = R20 × [1 + α × (T − 20)] calculated: R20 = ρ20 ÷ A
I = current (A), L = one-way route length (m; with a total conductor length the factor 2 is not used), R and X = resistance and reactance of one conductor (Ω/m), cos φ = power factor (DC: cos φ = 1, X = 0), T = conductor temperature (°C), A = cross-section (m²).
Copper: ρ20 = 1.7241 × 10⁻⁸ Ω·m, α = 0.00393 /°C. Aluminium: ρ20 = 2.8264 × 10⁻⁸ Ω·m, α = 0.00403 /°C. Power lost = I² × R × (total conductor length); three-phase: 3 × I² × R × L.
Worked example
A single-phase 230 V circuit, 2.5 mm² copper cable, 30 m one-way, carrying 16 A at power factor 1.
- IEC 60228 resistance at 20 °C: 7.41 Ω/km. At 70 °C: 7.41 × (1 + 0.00393 × 50) = 8.866 Ω/km
- Drop = 2 × 16 × 30 × 0.008866 = 8.51 V = 8.51 ÷ 230 = 3.70%
- Voltage at the load = 230 − 8.51 = 221.5 V; power lost = 16² × 0.008866 × 60 = 136 W
Three-phase 400 V, 16 mm² copper (1.15 Ω/km at 20 °C), 50 m, 40 A, cos φ = 1, at 20 °C: ΔV = √3 × 40 × 50 × 0.00115 = 3.98 V, which is 3.98 ÷ 400 = 1.0% of the line voltage.
Assumptions and limitations
- IEC 60228 values are the maximum DC resistances allowed for class 2 (stranded) conductors at 20 °C. Real cables are usually slightly lower, so the result is on the cautious side.
- “Calculated” sizes use the standard resistivity of copper or aluminium and the nominal cross-section. Real stranded conductors usually have a somewhat higher resistance than this, so the drop can be underestimated; prefer IEC 60228 values or the manufacturer’s data.
- AWG areas follow the standard AWG definition; resistance is calculated from that area. North American cable tables can differ slightly.
- DC resistance is used for AC. Skin and proximity effects, which raise the AC resistance of large cables, are not included. Reactance is included only if you enter it.
- Three-phase results assume a balanced load with no neutral current. The result is the line-to-line drop.
- The load current is taken as constant. Motor starting currents can be several times higher and give much larger temporary drops.
Safety note
This is an estimate of voltage drop only. It does not size cables or check current-carrying capacity, derating for grouping or ambient temperature, short-circuit ratings, protective devices or compliance with any wiring code. Electrical installations must be designed and checked by a qualified person to the rules that apply where you are.
References
- IEC 60228: Conductors of insulated cables — maximum DC resistance at 20 °C (class 2).
- IEC 60287-1-1: resistivity and temperature coefficient of copper and aluminium at 20 °C.
- Approximate voltage drop formula ΔV = k·I·L·(R cos φ + X sin φ), as used in IEC 60364-5-52 Annex G.
- AWG diameter definition (ASTM B258).