Formula & Calculator
Wire Resistance from Resistivity
Calculates a conductor's resistance from its material resistivity, length, and cross-sectional area.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R | Resistance | Ω |
| ρ | Resistivity | Ω·m |
| L | Length | m |
| A | Cross-sectional area | m² |
What it means
The resistance of a conductor is given by R = ρ·L / A, where ρ is the resistivity of the material (Ω·m), L is the length (m), and A is the cross‑sectional area (m²). This is the fundamental resistance formula used for wire sizing and material selection. Copper has low resistivity, making it preferred for wiring. Example: A copper wire of length 100m and cross‑section 2.5mm² (2.5×10⁻⁶ m²), with ρ = 1.68×10⁻⁸ Ω·m, has R = 1.68e-8 × 100 / 2.5e-6 = 1.68e-6 / 2.5e-6 = 0.672Ω. This resistance contributes to voltage drop and heating. Understanding this formula allows selection of wire gauge to meet resistance requirements.
Worked example
Wire Resistance from Resistivity – Practical Example
Real‑World| Parameter | Value |
|---|---|
| ρ | 1.68×10⁻⁸ Ω·m |
| L | 50 m |
| A | 2.5 mm² = 2.5×10⁻⁶ m² |
| Formula | R = ρ·L / A |
Common mistakes
Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.Applications
Wire resistance from resistivity R = ρ·L/A is the fundamental formula for conductor resistance. Engineers use it to calculate cable resistance, to size conductors, and to estimate power losses. This formula is essential for any electrical design involving conductors.
- Cable resistance and loss calculation
- Conductor sizing for power and voltage drop
- Material selection for conductivity
- Resistance and temperature coefficient analysis
- Educational understanding of conductor resistance