Wire Resistance Calculator
Find the resistance of a wire from its physical properties.
Calculate
Formulas
R = ρ × L / AR = Resistance, ρ = Resistivity, L = Length, A = Cross-sectional area
Wire Resistance
Every wire has resistance depending on material, length, and cross-section. Copper: 1.68×10⁻&sup8; Ω·m. Aluminum: 2.65×10⁻&sup8;. Steel: ~1.0×10⁻&sup7;.
Temperature effects
Copper resistance increases ~0.4% per °C. For critical applications, account for operating temperature.
How Wire Resistance Works
Every conductor opposes the flow of current to some degree. That opposition — resistance — depends on the material, how long the wire is, and how thick it is. The calculator uses the fundamental resistivity equation:
R = ρ × L / Aρ (rho) is the material resistivity, L is the wire length, and A is the cross-sectional area. Resistance rises with length and falls as the wire gets thicker.
Doubling the length doubles resistance; doubling the cross-sectional area halves it. This is why power cables for high currents are thick and kept as short as practical.
Worked Examples
A 50 m copper wire with 2.5 mm² cross-section. Copper resistivity is 1.68×10⁻⁸ Ω·m. Converting area to m² (2.5 mm² = 2.5×10⁻⁶ m²):
R = 1.68×10⁻⁸ × 50 / 2.5×10⁻⁶ = 0.336 Ω
Aluminium resistivity is 2.65×10⁻⁸ Ω·m, so the same geometry gives:
R = 2.65×10⁻⁸ × 50 / 2.5×10⁻⁶ = 0.530 Ω
About 58% more resistance — the price of aluminium's lower conductivity, offset by its lighter weight and lower cost.
Temperature Effects
Resistivity rises with temperature in metals. Copper increases roughly 0.4% per °C. A wire that measures 1 Ω at 20 °C will read about 1.13 Ω at 50 °C. For circuits that run warm — motor windings, power resistors, automotive harnesses — account for the operating temperature rather than the room-temperature value.
Resistivity of Common Materials
| Material | Resistivity (Ω·m at 20°C) | Relative to copper |
|---|---|---|
| Silver | 1.59×10⁻⁸ | 0.95× |
| Copper | 1.68×10⁻⁸ | 1.00× |
| Aluminium | 2.65×10⁻⁸ | 1.58× |
| Steel | ~1.0×10⁻⁷ | ~6× |
Silver conducts marginally better than copper but is far too expensive for general wiring. Copper is the practical standard for most applications.
Frequently Asked Questions
What units should I use?
Keep units consistent. If resistivity is in Ω·m, length must be in metres and area in m². If you prefer Ω·mm²/m for resistivity, then area can stay in mm² and length in m.
Why does thicker wire have less resistance?
A larger cross-section gives current more parallel paths to flow through, lowering the overall opposition — just as a wider pipe carries water with less restriction.
Does wire shape matter, or just area?
For DC and low frequencies, only the cross-sectional area matters. At high frequencies the skin effect pushes current toward the surface, effectively raising resistance.