Key takeaways
- R = ρ × L ÷ A — resistance from material, length and area.
- Copper resistance rises roughly 0.4% per °C.
- A conductor at 70 °C has about 20% more resistance than at 20 °C.
- Aluminium needs about 64% more cross-section for the same resistance.
What resistivity means
Resistivity (ρ, rho) is a property of the material itself, independent of shape. It is the resistance of a cube of the material one metre on each side, measured face to face, in ohm-metres.
Resistance then depends on geometry:
- R = ρ × L ÷ A
Longer means more resistance; thicker means less. Doubling the length doubles R; doubling the area halves it.
Values for common conductors
| Material | ρ (Ω·m) | α (per °C) | Notes |
|---|---|---|---|
| Silver | 1.59 × 10⁻⁸ | 0.0038 | Best conductor, cost prohibitive |
| Copper (annealed) | 1.72 × 10⁻⁸ | 0.00393 | The wiring standard |
| Gold | 2.44 × 10⁻⁸ | 0.0034 | Contacts, corrosion resistance |
| Aluminium | 2.82 × 10⁻⁸ | 0.0039 | Light, used for overhead lines |
| Tungsten | 5.60 × 10⁻⁸ | 0.0045 | Lamp filaments |
| Iron | 9.71 × 10⁻⁸ | 0.0050 | Structural, poor conductor |
| Nichrome | 1.10 × 10⁻⁶ | 0.0004 | Heating elements, stable with heat |
Worked example
A 30 m length of 2.5 mm² copper cable:
- Convert the area: 2.5 mm² = 2.5 × 10⁻⁶ m²
- R = (1.72 × 10⁻⁸ × 30) ÷ (2.5 × 10⁻⁶)
- R = 0.206 Ω per conductor
- For a circuit, double it — out and back → 0.413 Ω
At 20 A that loop resistance costs 8.3 V and dissipates 165 W. Our voltage drop guide works through the consequences.
Conductor Resistance CalculatorChoose a material, length and cross-section to get resistance, with an optional temperature correction.
The temperature correction
Metals conduct worse when hot. The lattice vibrates more, electrons scatter more often, and resistance rises:
- Rₜ = R₂₀ × [1 + α(T − 20)]
For copper, α = 0.00393 per °C.
How much difference does it make?
| Temperature | Resistance | Change |
|---|---|---|
| −20 °C | 0.843 Ω | −15.7% |
| 0 °C | 0.921 Ω | −7.9% |
| 20 °C | 1.000 Ω | reference |
| 50 °C | 1.118 Ω | +11.8% |
| 70 °C | 1.197 Ω | +19.7% |
| 90 °C | 1.275 Ω | +27.5% |
This is why a cable run that calculates at 2.6% drop when cold can exceed 3% at full load. Designers often check the drop at the conductor's rated operating temperature rather than at 20 °C.
Where the effect shows up
- Motor windings. Measuring winding resistance is a standard way to infer temperature rise.
- Filament lamps. Tungsten's high α means a cold filament measures a fraction of its hot resistance, which is why lamps draw a large inrush current.
- Shunts and current sensing. Precision shunts use manganin, whose α is near zero, so the reading does not drift as it heats.
- Heating elements. Nichrome is chosen partly because its resistance barely changes across its huge working range.
Conductivity, the other way round
Conductivity (σ) is simply 1 ÷ ρ. Cable is often specified by percentage IACS — International Annealed Copper Standard — where pure annealed copper is 100%. Modern electrolytic copper reaches about 101%, and typical aluminium alloy around 61%.
Using resistance to measure temperature
Because the relationship between copper resistance and temperature is so predictable, it works in reverse: measure resistance and you can infer temperature.
Rearranging the correction gives:
- T = 20 + (Rₜ ÷ R₂₀ − 1) ÷ α
A motor winding measuring 1.0 Ω cold and 1.18 Ω after a run has risen to about 66 °C. This resistance method is the standard way of establishing the average temperature rise of a winding, because it reports the whole conductor rather than one point a probe happens to touch.
Where the same principle is used deliberately
- Platinum RTDs such as the Pt100 exploit an extremely stable temperature coefficient.
- Thermistors use semiconductors with a far larger, non-linear coefficient for sensitive detection.
- Fuse elements rely on resistance rising with heat to accelerate their own melting.
Putting it to work
Resistivity is where cable sizing starts. Once you have the conductor resistance, the ohms law formulas give the drop and the heat, and wire gauge amp rating covers the thermal limit. The conductor resistance calculator combines all three inputs in one place.
Frequently asked questions
What is the resistivity of copper?
About 1.72 × 10⁻⁸ Ω·m for annealed copper at 20 °C. Hard-drawn copper is very slightly higher, around 1.77 × 10⁻⁸ Ω·m.
How much does copper resistance change with temperature?
Roughly 0.393% per degree Celsius. A conductor running at 70 °C has about 20% more resistance than the same conductor at 20 °C.
Why is aluminium used for power lines if copper conducts better?
Aluminium is around a third of the weight for the same conductance and much cheaper. On overhead lines, where weight drives tower cost, that outweighs the need for a larger cross-section.