Work out the resistance of a copper or aluminium conductor run from its cross-section, length and operating temperature.
Resistance at 20 °C
1.379Ω
Check the values to see a result.
Annealed copper, DC resistance from the nominal cross-section. Skin effect on large AC conductors is not included.
R20 = ρ20 × L ÷ ART = R20 × (K + T) ÷ (K + 20), with K = 234.5 for copper and 228 for aluminium
200 m of 2.5 mm² copper has a resistance of 1.379 Ω at 20 °C.
Tip: For a two-wire circuit the current flows out and back, so count the loop, not the one-way length.
The resistance of a wire is its resistivity times its length divided by its cross-section, corrected for temperature. 100 m of 2.5 mm² copper, out and back, is 1.379 Ω at 20 °C. Use it for the loop resistance of a CT secondary, a sensor cable or a DC supply, and for the IR drop and I²R loss at a given current.
R20 = ρ20 × L ÷ A
ρ20 is 0.017241 Ω·mm²/m for annealed copper (100% IACS) and 0.02826 Ω·mm²/m for 61% conductivity aluminium. L is the conductor length in metres, twice the route for a loop, and A the cross-section in mm².
RT = R20 × (K + T) ÷ (K + 20)
K is 234.5 for copper and 228 for aluminium. Copper at 70 °C, the limit for PVC insulation, has about 20% more resistance than at 20 °C.
ΔV = I × R; P = I2 × R
With a current entered, the calculator gives the resistive drop along the conductors and the heat they dissipate.
These are figures for the nominal cross-section. Cable standards such as IEC 60228 set a maximum resistance per size, which is a little above the nominal figure, so the voltage drop calculator uses the IEC maxima for standard cables.
Out and back is 200 m of conductor: 0.017241 × 200 ÷ 2.5 = 1.379 Ω at 20 °C. On a 5 A CT secondary that loop alone would use 5² × 1.379 = about 34 VA of burden, far more than most CTs allow.
Resistance at 20 °C 1.379 Ω Open in the calculator
The loop is 100 m, 1.149 Ω at 20 °C and 1.375 Ω hot. At 10 A it drops 13.75 V and dissipates 137.5 W along its length.
Resistance at 70 °C 1.375 Ω Open in the calculator
12 AWG is 3.309 mm². A 100 ft run is 60.96 m of conductor out and back, which is 0.3176 Ω at 20 °C.
Resistance at 20 °C 0.3176 Ω Open in the calculator
Resistance of one conductor per kilometre from nominal cross-section. Divide by 10 for 100 m.
| Size (mm²) | Copper, 20 °C (Ω/km) | Copper, 70 °C (Ω/km) | Aluminium, 20 °C (Ω/km) |
|---|---|---|---|
| 0.5 | 34.5 | 41.3 | 56.5 |
| 0.75 | 23 | 27.5 | 37.7 |
| 1 | 17.2 | 20.6 | 28.3 |
| 1.5 | 11.5 | 13.8 | 18.8 |
| 2.5 | 6.9 | 8.25 | 11.3 |
| 4 | 4.31 | 5.16 | 7.07 |
| 6 | 2.87 | 3.44 | 4.71 |
| 10 | 1.72 | 2.06 | 2.83 |
| 16 | 1.08 | 1.29 | 1.77 |
| 25 | 0.69 | 0.825 | 1.13 |
| 35 | 0.493 | 0.589 | 0.808 |
| 50 | 0.345 | 0.413 | 0.565 |
| 70 | 0.246 | 0.295 | 0.404 |
| 95 | 0.181 | 0.217 | 0.298 |
| 120 | 0.144 | 0.172 | 0.236 |
| 150 | 0.115 | 0.138 | 0.188 |
| 185 | 0.0932 | 0.112 | 0.153 |
| 240 | 0.0718 | 0.086 | 0.118 |
0.017241 Ω divided by the cross-section in mm², at 20 °C: 11.49 mΩ for 1.5 mm², 6.9 mΩ for 2.5 mm² and 4.31 mΩ for 4 mm².
Twice for a circuit, because current flows out on one conductor and back on the other. Choose “One conductor” when you need the resistance of a single wire, such as one line of a three-phase feeder.
Aluminium conducts about 61% as well as copper, so it needs roughly 1.6 times the cross-section for the same resistance. It is lighter and cheaper per ampere, which is why large feeders often use it.