Electrical and electronics
Cable voltage drop calculator (DC, single-phase and three-phase)
Estimate voltage drop in copper or aluminium cable for DC, single-phase and three-phase circuits, with resistivity corrected for conductor temperature and optional reactance.
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Result
A 6.44% drop exceeds the 5% commonly recommended for a whole installation (3% for lighting circuits in IEC 60364-5-52 Annex G for a public supply; the US NEC informational notes suggest 3% per branch and 5% overall).
- Copper (annealed, 100% IACS): ρ₂₀ = 0.017241 Ω·mm²/m, α₂₀ = 0.00393 /K, R(T) = ρ₂₀ (1 + α₂₀ (T − 20 °C)) / A.
- ΔV = 2 × I × L × (R cos φ + X sin φ) with L the one-way length.
- This estimates the drop only. It does not check ampacity, installation method, grouping, short-circuit or protective-device rules; size cables with your local wiring code and the cable maker’s data.
Method and limits
The drop along a run of one-way length L carrying current I is
ΔV = k × I × L × (R cos φ + X sin φ)
with k = 2 for DC and single-phase circuits (current flows out and back) and k = √3 for a balanced three-phase circuit (giving the line-to-line drop). For DC, cos φ = 1 and X = 0. R is the resistance of one conductor per metre at its operating temperature:
R(T) = ρ20 (1 + α20 (T − 20 °C)) / A
using ρ20 = 0.017241 Ω·mm²/m and α20 = 0.00393 /K for annealed copper (IEC 60028) and ρ20 = 0.028264 Ω·mm²/m and α20 = 0.00403 /K for aluminium (IEC 60889).
Worked example: a 120 V single-phase circuit, 20 A, 100 ft one-way of 12 AWG copper at 75 °C. R = 1.93 Ω per 1000 ft (the NEC Chapter 9 Table 8 value), so ΔV = 2 × 20 A × 100 ft × 1.93 Ω/1000 ft = 7.73 V, 6.4% of 120 V: too much for the 3% branch-circuit guidance.
The power lost in the cable is the number of current-carrying conductors × I² R L.
Limits
Steady current, a balanced three-phase load and uniform conductor temperature are assumed; skin and proximity effects (significant above about 150 mm² at 50/60 Hz) and harmonic currents are ignored. Typical limits are 3% for a branch circuit and 5% overall (NEC informational notes), or 3% for lighting and 5% for other uses from a public supply (IEC 60364-5-52 Annex G). This tool does not check current-carrying capacity, installation method, grouping, fault loop impedance or protective devices.
References
- NFPA 70 (National Electrical Code): Chapter 9 Table 8 conductor properties and the voltage-drop informational notes
- Schneider Electric Electrical Installation Guide (IEC 60364 practice, voltage-drop limits and formula)
- Voltage drop: DC and AC formulas
- Electrical resistivity and its temperature coefficient (copper 1.724 × 10⁻⁸ Ω·m, α = 0.00393 /K)
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