Voltage drop over a DC, single-phase or three-phase cable run, plus AWG wire size to diameter, mm², kcmil and resistance per km, and back.
By AdminDrafted with AI writing toolsUpdated Checked examples: 6
30 m of 12 AWG copper carrying 15 A drops 4.69 V (3.91% of 120 V), leaving 115.31 V at the load and wasting 70.34 W as heat.
The current flows out and back, so the wire length counts twice; reactance is ignored.
Voltage drop is the voltage lost along a cable because the conductor has resistance. The calculator takes the resistance per metre from the cross-section (R′ = ρ/A, with ρ at 20 °C) and multiplies it by the current and the one-way length: twice for DC and single-phase, because the current goes out and back, and by √3 for a balanced three-phase run. It also converts any AWG size to diameter, mm², kcmil and ohms per km with the ASTM B258 formula, or finds the nearest AWG for a measured diameter.
The default, 15 A over 30 m of 12 AWG copper at 120 V, drops 4.69 V, or 3.91%. That is above the 3% branch-circuit figure in the NEC informational note; 10 AWG brings the same run down to 2.46%.
The result is a resistive estimate at 20 °C. Copper's resistance is about 22% higher at a 75 °C operating temperature, and long AC runs of large cables add reactance, so leave a margin when the result is close to a limit.
For DC or single-phase AC, ΔV = 2 × I × R′ × L, where R′ is the wire's resistance per meter and L the one-way length. 15 A over 30 m of 12 AWG copper (5.211 Ω/km at 20 °C) drops 2 × 15 × 0.005211 × 30 = 4.69 V, which is 3.91% of 120 V.
For a balanced three-phase load, use ΔV = √3 × I × R′ × L with the line current, and compare the result with the line-to-line voltage. 60 A over 50 m of 4 AWG aluminum at 400 V drops 6.94 V, or 1.74%.
ASTM B258 defines the gauge by formula: d = 0.005 in × 92^((36 − n)/39), with 1/0 to 4/0 counted as n = 0 to −3. That makes 36 AWG exactly 0.005 in and 4/0 exactly 0.46 in.
Each gauge number changes the diameter by a factor of 1.1229, so three gauge numbers double or halve the area. Solid copper at 20 °C:
NIST's historic wire-gage table and Wikipedia's AWG table give nominal diameters and areas to compare. Area in kcmil is the diameter in mils squared, divided by 1,000; a mil is a thousandth of an inch.
To identify a measured wire, invert the formula: n = 36 − 39 × log₉₂(d / 0.127 mm). A 2.05 mm conductor gives n = 12.01, so it is 12 AWG. Measure the bare metal; the insulation's outside diameter says nothing about the gauge.
Electrical-grade aluminum has a resistivity of 0.028264 Ω·mm²/m at 20 °C (61% IACS, IEC 60889), 1.64 times copper's. The same 15 A, 30 m run in 12 AWG drops 6.41% in aluminum against 3.91% in copper.
Matching copper's resistance takes about 1.6 times the cross-section, roughly two AWG sizes larger. Aluminum terminations need connectors rated for aluminum.
An informational note to NEC 210.19(A) recommends at most 3% on a branch circuit and 5% for feeder and branch combined. The note is advice, though some jurisdictions adopt it.
The rows below are the 12 AWG copper run above (Default), the same run in 10 AWG (Larger wire), and the same run carrying no current (No current).
| Scenario | Voltage drop |
|---|---|
| Default | 3.91% |
| Larger wire | 2.46% |
| No current | 0.00% |
12 AWG misses the 3% branch figure and 10 AWG meets it. With no current there is no drop at all, because ΔV is proportional to I.
Rearrange for the longest one-way run within a limit, written as a fraction: L = (limit × V)/(2 × I × R′). At 15 A on 120 V with a 3% limit, 12 AWG copper reaches 23.03 m (75.6 ft) and 10 AWG reaches 36.62 m (120.1 ft).
A wire can pass a voltage-drop check and still be too small to carry its current safely. Size the conductor first for ampacity, insulation temperature rating and terminal ratings under your electrical code, then check the drop.
The drop itself is a resistive estimate at 20 °C. A copper conductor running at 75 °C has about 22% more resistance, and long AC runs of large cables add reactance, so leave margin when a result is close to a limit.
The Ohm's law calculator checks the current and resistance behind a drop. To price the watts a cable wastes, use the electricity cost calculator.
Checked against: 0.005 in × 92^(24/39) = 2.0525254 mm; ρ/A with ρ = 1.7241e-8 Ω·m (AWG table: 2.053 mm, 3.31 mm², 5.211 Ω/km)
Checked against: ASTM B258 definition: 4/0 = 0.4600 in = 211.6 kcmil
Checked against: ASTM B258 definition: 36 AWG = 0.0050 in
Checked against: n = 36 − 39·log₉₂(2.05/0.127) = 12.0106
In the US, an informational note to NEC 210.19 recommends at most 3% on a branch circuit and 5% in total for feeder plus branch circuit. The note is advice, not an enforceable rule, although some jurisdictions adopt it. IEC 60364-5-52 and BS 7671 give 3% for lighting and 5% for other loads when the installation is fed from a public low-voltage network, and 6% and 8% from a private supply.
Multiply the current by the resistance of the wire that carries it. For DC or single-phase, ΔV = 2 × I × R′ × L, where R′ is the resistance per metre and L the one-way length; the 2 counts the outgoing and return conductors. For balanced three-phase, use √3 (1.732) instead of 2 and compare the result with the line-to-line voltage. 15 A over 30 m of 12 AWG copper (5.21 Ω/km) drops 4.69 V.
ASTM B258 defines AWG by a formula: 36 AWG is 0.005 in and 4/0 (0000) is 0.46 in, with 39 equal ratio steps between them, so each gauge number changes the diameter by a factor of 1.1229. Three gauge numbers double or halve the cross-sectional area, and six double or halve the diameter. 12 AWG is 2.053 mm across with 3.31 mm² of metal.
Table 8 lists DC resistance at 75 °C, while this calculator uses solid conductors at 20 °C with copper's resistivity from IEC 60028 (0.017241 Ω·mm²/m). For solid 12 AWG copper, Table 8 gives 1.93 Ω per 1000 ft against 1.59 here; the whole difference is the 55 °C of extra temperature. Stranded 12 AWG is listed slightly higher, at 1.98 Ω per 1000 ft.
About 1.6 times the cross-section, or roughly two AWG sizes larger, for the same resistance and voltage drop. Electrical-grade aluminium conducts 61% as well as copper (IEC 60889), with a resistivity of 0.028264 Ω·mm²/m against copper's 0.017241. The final size must also meet the ampacity tables, and aluminium terminations need connectors rated for it.
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