Wire Resistance Calculator
Calculate wire resistance from material, length, and AWG gauge using R = rL/A.
Covers copper, aluminum, silver, and gold in imperial and metric units.
Wire resistance is the opposition to electrical current flow in a conductor. It depends on the material, length, and cross-sectional area of the wire. Understanding resistance is essential for electrical engineering, electronics, and safely sizing wiring in buildings and appliances.
Core formula (Ohm’s Law): V = I × R Where V = Voltage (volts), I = Current (amperes), R = Resistance (ohms, Ω)
Wire Resistance formula: R = ρ × L ÷ A
Where:
- R = resistance in ohms (Ω)
- ρ (rho) = resistivity of the material (Ω·m), a property of the conductor material
- L = length of the wire in meters
- A = cross-sectional area in square meters
Derived formulas: Current: I = V ÷ R Voltage: V = I × R Power dissipated: P = I² × R (watts lost as heat)
What each variable means:
- Resistivity (ρ): a material constant. Copper: 1.72 × 10⁻⁸ Ω·m. Aluminum: 2.82 × 10⁻⁸ Ω·m. Silver (lowest): 1.59 × 10⁻⁸ Ω·m. Resistance wire (nichrome): 110 × 10⁻⁸ Ω·m.
- Length: longer wire = more resistance (proportional relationship).
- Cross-sectional area: thicker wire = less resistance (inverse relationship). Doubling diameter reduces resistance by 75%.
- Temperature effect: resistance increases with temperature for most metals: R = R₀ × [1 + α × (T − T₀)], where α is the temperature coefficient.
AWG wire gauge reference (copper):
| AWG | Diameter (mm) | Resistance (Ω/km) | Max Current |
|---|---|---|---|
| 14 AWG | 1.63 mm | 8.28 Ω/km | 15A |
| 12 AWG | 2.05 mm | 5.21 Ω/km | 20A |
| 10 AWG | 2.59 mm | 3.28 Ω/km | 30A |
| 8 AWG | 3.26 mm | 2.06 Ω/km | 40A |
Worked example: A 50-meter copper wire (AWG 14, A = 2.08 mm² = 2.08 × 10⁻⁶ m²) carries 12A at 120V.
R = 1.72 × 10⁻⁸ × 50 ÷ 2.08 × 10⁻⁶ = 0.414 Ω Voltage drop = 12A × 0.414 Ω = 4.97 V drop (4.1% of 120V — acceptable; keep under 5%) Power lost as heat = 12² × 0.414 = 59.6 watts of wasted energy