Voltage Drop

A conductor of cross-section A has resistance per length R₂₀ = ρ₂₀ ÷ A at 20 °C, and R(T) = R₂₀ × (1 + α₂₀ (T − 20)) at conductor temperature T. For DC and single-phase AC the current goes out and comes back, so the drop is V = 2 × I × R(T) × L with L the one-way length; for a balanced three-phase load it is V = √3 × I × R(T) × L. Conductors in parallel per phase divide the resistance. The percent figure is the drop divided by the source voltage; the voltage at the load is the difference. If you give a target, the page also reports the longest run at your size and the smallest listed size that meets the target at your length.

Copper is the International Annealed Copper Standard: 0.017241 Ω·mm²/m at 20 °C with a temperature coefficient of 0.00393 per °C, as printed in NBS Handbook 100, Copper Wire Tables (US National Bureau of Standards, 1966), a public-domain document. AWG sizes follow the gauge law in the same handbook — 0.4600 in at 4/0 to 0.0050 in at No. 36 in 38 geometric steps — and the tests check the computed resistances against its Table 5. Aluminium uses the 61 % IACS conductor grade (0.028264 Ω·mm²/m, 0.00403 per °C) as commonly published; the standards that define it are licensed and were not consulted, so for aluminium in particular prefer the datasheet entry. Metric sizes are the nominal IEC 60228 series. Resistance is computed from the nominal area as a solid conductor; stranded cable measures a few percent higher, and a cable's datasheet Ω/km, entered in step 03, replaces the computation exactly.

Resistance rises about 0.4 % per °C: a conductor at 75 °C has 22 % more resistance than at 20 °C, so the drop is 22 % higher. The default of 75 °C is a common conductor operating temperature used in voltage-drop tables; it is an assumption you can change, not a measured value. A lightly loaded cable runs cooler than its rating and the true drop is lower; use the temperature your conductor will actually reach.

This is a resistive calculation: reactance is neglected and the load is treated as resistive (power factor 1). That is accurate for small and medium conductors; for AC on conductors above about 50 mm² (1/0 AWG), or at low power factor, the real drop is higher. Nothing here is a conductor selection: ampacity, overcurrent protection, derating, and the drop your installation may allow are set by the code that applies to you (NEC, IEC 60364, BS 7671, AS/NZS 3008 and others), and those tables are not reproduced on this site. Inputs stay in your browser; the same four anonymous usage counts as the rest of the site apply.