Wire Resistance Calculator Formula
Understand the math behind the wire resistance calculator. Each variable explained with a worked example.
Formulas Used
Wire Resistance
wire_resistance = resistivity * wire_length / (area * 1e-6)Variables
| Variable | Description | Default |
|---|---|---|
resistivity | Resistivity (ρ)(Ω·m) | 1.68e-8 |
wire_length | Wire Length(m) | 100 |
area | Cross-Sectional Area(mm²) | 2.5 |
How It Works
Wire Resistance
The resistance of a wire depends on the material, its length, and cross-sectional area.
Formula
R = ρ * L / A
where ρ is the resistivity of the material (Ω·m), L is the wire length, and A is the cross-sectional area. Copper has ρ = 1.68 x 10^-8 Ω·m.
Worked Example
100 m of copper wire with 2.5 mm² cross-section.
resistivity = 1.68e-8wire_length = 100area = 2.5
- 01R = ρ * L / A
- 02R = 1.68e-8 * 100 / 2.5e-6
- 03R = 1.68e-6 / 2.5e-6
- 04R = 0.672 Ω
Frequently Asked Questions
What is the resistivity of common conductors?
Copper: 1.68e-8, aluminum: 2.65e-8, silver: 1.59e-8, gold: 2.44e-8 (all in Ω·m at 20°C).
How does wire length affect resistance?
Resistance is proportional to length. Doubling the wire length doubles the resistance.
Why use thicker wire for high current?
A larger cross-section reduces resistance and thus reduces I²R heating losses and voltage drops.
Ready to run the numbers?
Open Wire Resistance Calculator