Wire Resistance Calculator

Resistance separates the material from the shape

R = ρL/A splits a conductor’s resistance into two independent parts. Resistivity ρ is a property of the material alone: it is what copper is, whether drawn into a hair-thin strand or cast into a bar. Length and cross-section are the geometry you choose. Resistance rises in proportion to length because the carriers have further to travel against the lattice, and falls in proportion to area because a wider conductor offers more parallel paths.

That inverse relationship with area catches people out, because cable is sold by diameter while the formula wants area. Doubling the diameter quadruples the area and so quarters the resistance. Resistivity here is quoted in microohm centimetres at 20 °C, the convention used in materials tables: copper 1.678, aluminium 2.65, gold 2.44, iron 9.71 and nichrome 110. Nichrome is about 66 times as resistive as copper, which is why it makes heating elements and copper does not.

Worked example

Thirty metres of 1 mm² annealed copper, the values loaded above.

• Convert the resistivity: 1.678 µΩ·cm = 1.678 × 10⁻⁸ Ω·m
• Convert the area: 1 mm² = 1 × 10⁻⁶ m²
• R = (1.678 × 10⁻⁸ × 30) / (1 × 10⁻⁶)
• R = 0.5034 Ω, which is 16.78 Ω/km
• Drop at 10 A: V = IR = 10 × 0.5034 = 5.034 V

A solid round conductor of that cross-section would be 1.128 mm across, from d = 2√(A/π). The 5.034 V figure is 2.2 percent of a 230 V supply, which is the number an installer cares about, and it is close to the limits most wiring rules set for a final circuit.

The two corrections real cable runs need

First, use the total conductor length, not the distance to the load. Current goes out along one core and returns along the other, so a socket 15 metres away is 30 metres of copper. Entering the one-way figure halves the calculated drop, and it is the single most common error in cable sizing.

Second, correct for temperature. Copper’s resistance rises about 0.393 percent per degree Celsius, and the tabulated resistivity is a 20 °C figure. A conductor working at 70 °C, unremarkable for insulated cable in a bunched run, sits 50 degrees above that and so carries roughly 20 percent more resistance: the example above becomes about 0.602 Ω and drops 6.02 V at 10 A. The effect is self-reinforcing, since a higher resistance dissipates more heat at the same current.

Aluminium is the standard choice for overhead transmission despite 1.6 times the resistivity of copper. Matching a copper conductor’s resistance takes about 1.6 times the cross-section, but aluminium is roughly a third of the density, so the aluminium conductor still weighs under half as much. For a span hanging between towers, mass per metre sets the cost, and conductivity per unit volume is not the figure that binds.

Common mistakes

• Using the one-way distance. Double it for any voltage-drop calculation on a two-core run. The length field wants the full path.
• Entering a diameter where the area belongs. A 2 mm wire is not 2 mm². Its area is π(1 mm)² = 3.14 mm², and getting this wrong scales the answer by whatever the squared factor happens to be.
• Mixing centimetre and metre resistivity units. One microohm centimetre is 10⁻⁸ Ω·m, not 10⁻⁶. Check which convention a quoted figure uses before trusting it.
• Ignoring operating temperature. A cable already close to its drop limit at 20 °C will exceed it when warm. Design against the hot resistance, not the table value.
• Assuming resistance sets the current limit. It sets the voltage drop. Current capacity is a thermal question about insulation and heat shedding, and a run can pass the drop check while still being too thin to carry the load safely.

Converting units first? Use the length, resistance, area and resistivity conversion tables.