Case 1
- Resistivity ρ (Ω·m)
- 1.68e-8Ω·m
- Length L (m)
- 10m
- Cross-sectional area A (m²)
- 0.000001m²
0.168000Ω
Open with these valuesWire Resistance Calculator
0.168000Ω
Result: 0.168000 ΩTen metres of 1 mm² copper wire has 0.168 Ω. Resistance is the resistivity times the length divided by the cross-section, so a longer or thinner wire resists more and a shorter or thicker one resists less. Everything stays in SI units, and 1 mm² is 0.000001 m².
Worked examples
Case 2
- Resistivity ρ (Ω·m)
- 2.82e-8Ω·m
- Length L (m)
- 10m
- Cross-sectional area A (m²)
- 0.000001m²
0.282000Ω
Open with these valuesCase 3
- Resistivity ρ (Ω·m)
- 1.68e-8Ω·m
- Length L (m)
- 100m
- Cross-sectional area A (m²)
- 0.000002m²
0.840000Ω
Open with these valuesHow it's calculated
R = ρ × L / A
- StepEnter the resistivity in ohm-metres — copper is 0.0000000168 at 20 °C.
- StepEnter the wire length in metres, measured along one conductor.
- StepEnter the cross-section in square metres: 1 mm² is 0.000001 m².
- ResultRead the resistance in ohms.
Reference table
| ρ, length, area | What that is | Resistance (Ω) |
|---|---|---|
| 0.0000000168, 10, 0.000001 | 10 m of 1 mm² copper | 0.168 |
| 0.0000000244, 5, 0.0000005 | 5 m of 0.5 mm² gold | 0.244 |
| 0.0000000282, 10, 0.000001 | 10 m of 1 mm² aluminium | 0.282 |
| 0.0000000168, 100, 0.000002 | 100 m of 2 mm² copper | 0.840 |
| 0.000001, 1, 1 | the unit cube, one metre a side | 0.000001 |
Questions
How do I calculate wire resistance?
Multiply the material's resistivity by the wire length and divide by the cross-sectional area: R = ρ × L / A. Use ohm-metres, metres and square metres, and the result comes out in ohms. Ten metres of 1 mm² copper wire has 0.168 Ω.
What is resistivity?
Resistivity is a material property measuring how strongly a material opposes current, in ohm-metres, and it does not depend on the wire's shape. At 20 °C copper is about 0.0000000168 Ω·m, aluminium about 0.0000000282 and gold about 0.0000000244. That is why copper and aluminium are the standard choices for wiring.
Why does a thicker wire have less resistance?
Because the cross-sectional area sits in the denominator of R = ρL/A. A wider conductor gives the current more room, so doubling the area halves the resistance. That is why high-current circuits use thick cables.
How do I convert mm² to m² for the area?
Divide the area in square millimetres by one million. One square millimetre is 0.000001 m², so a common 1.5 mm² house wire is 0.0000015 m². Entering the area in mm² instead makes the answer wrong by a factor of a million.
Does temperature affect the resistance?
Yes, the resistivity of metals rises with temperature, so a hot wire resists slightly more than a cold one. This calculator uses the single resistivity you enter, and the standard table figures are quoted at 20 °C. For precise work at another temperature, enter the resistivity for that temperature.
Sources and last check
Information, not professional advice.