What is the formula for wire resistance?

R = ρL/A, where ρ (rho) is the resistivity of the material in Ω·m, L is the wire length in meters, and A is the cross-sectional area in m². A higher resistivity, longer wire, or smaller area all increase resistance.

Resistivity (ρ) is a material property measured in ohm-meters (Ω·m). It describes how strongly a material opposes the flow of electric current. Copper has very low resistivity (~1.68×10⁻⁸ Ω·m); nichrome has high resistivity (~1.1×10⁻⁶ Ω·m).

How does wire diameter affect resistance?

Resistance is inversely proportional to cross-sectional area. Doubling the diameter quadruples the area, cutting resistance to one quarter. A thinner wire always has higher resistance than a thicker wire of the same material and length.

Why does temperature affect resistance?

This calculator uses standard room-temperature (20 °C) resistivity values. In practice, resistivity increases with temperature for metals. For high-precision work, apply a temperature coefficient correction: ρ_T = ρ₀[1 + α(T − 20)].

What units does this calculator use?

Length is entered in meters or centimeters, area in mm² (most practical for wires), and resistivity in Ω·m. The result is displayed in ohms with auto-scaling to mΩ, kΩ, or MΩ as needed.

Resistance of Wire Calculator

Name: Resistance of Wire Calculator
Availability: InStock
Author: Nham Vu

Compute wire resistance from resistivity, length, and cross-sectional area using R = ρL/A.

Wire Parameters

Material preset

Resistivity ρ (Ω·m)

Scientific notation accepted: 1.68e-8

Wire length

Cross-section input mode

Cross-sectional area (mm²)

Result

Enter wire parameters and click Calculate.

Formula reference

R = ρL / A

RResistance (Ω)

ρ (rho)Resistivity (Ω·m)

LLength (m)

ACross-sectional area (m²)

Summary

Compute wire resistance from resistivity, length, and cross-sectional area using R = ρL/A.

How it works

Select a material from the preset list or enter a custom resistivity value.
Enter the wire length in meters (or adjust the unit).
Enter the cross-sectional area in mm² (or switch to radius/diameter input).
The resistance R = ρL/A is computed instantly.
Results are shown in ohms, with automatic unit scaling to mΩ, kΩ, or MΩ.

Use cases

Size wiring for electrical projects and PCB traces.
Estimate voltage drop over long cable runs.
Verify datasheet resistance values for common conductors.
Teach or study the relationship between wire geometry and resistance.
Compare resistance of different materials at the same dimensions.
Calculate heat dissipation in resistive heating elements.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu