Wire Resistance Calculator

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):

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