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, measured at 20°C. Copper: 1.72 × 10⁻⁸ Ω·m. Aluminum: 2.82 × 10⁻⁸ Ω·m. Silver, the lowest of any metal: 1.59 × 10⁻⁸ Ω·m. Gold: 2.44 × 10⁻⁸ Ω·m. Steel: 1.43 × 10⁻⁷ Ω·m. Resistance wire (nichrome): 110 × 10⁻⁸ Ω·m. Silver beats copper by only 8%, which is nowhere near enough to justify the price, and gold is worse than copper outright. Gold is used on contacts because it does not corrode, not because it conducts well.
• 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, and the mistake almost everyone makes

A 50-metre run of AWG 14 copper (A = 2.08 mm² = 2.08 × 10⁻⁶ m²) feeding a load that draws 12 A from a 120 V supply.

R for one conductor = 1.72 × 10⁻⁸ × 50 ÷ (2.08 × 10⁻⁶) = 0.413 Ω

Here is the part that gets skipped. Current has to get there and come back. A 50 m run is 100 m of conductor, so the resistance the current actually sees is 0.827 Ω, not 0.413.

Voltage drop = 12 A × 0.827 Ω = 9.9 V, which is 8.3% of 120 V

Most electrical codes want under 3% on a branch circuit and under 5% overall, so AWG 14 is the wrong choice for this run. Halve the resistance by stepping up to AWG 11, or in practice AWG 10, and the drop falls to about 3.3%. Power wasted as heat = 12² × 0.827 = 119 watts, which is both a bill and a fire-safety consideration inside a wall.

Use the one-way run length in the calculator below. It does the doubling for you.