Wire Resistance
R = ρ × L / A
Quick answer
This calculator solves R = ρ × L / A for Resistance. With Resistivity (Ω·m) 1 × 10⁻⁶ Ω·m, Length 1 m, Cross-Section Area 10 mm², the result is 100 mΩ. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Wire resistance depends on the material's resistivity, the wire length, and its cross-sectional area. Copper is the most common conductor with ρ = 1.724 × 10⁻⁸ Ω·m at 20°C. Aluminum has ρ = 2.65 × 10⁻⁸ Ω·m (about 60% of copper's conductivity). Longer wires and thinner wires have higher resistance. This resistance causes voltage drops and power losses (I²R heating) that must be accounted for in power distribution, speaker wiring, motor cables, and any application where current flows over significant distances.
Variables
- R — Wire resistance (Ω)
- ρ — Resistivity of the conductor material (Ω·m)
- L — Wire length (m)
- A — Cross-sectional area (m²)
Practical Notes
Resistivity increases with temperature. Copper has a temperature coefficient of +0.00393/°C, meaning resistance increases about 0.4% per degree C. For a 10m run of 16 AWG copper wire (A = 1.31 mm²), R ≈ 0.132Ω. At 5A, this drops 0.66V and dissipates 3.3W per conductor. Remember to account for both supply and return conductors.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R | Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| rho | Resistivity (Ω·m) | Ω·m | Ω·m |
| L | Length | m | mm, cm, m, km |
| A | Cross-Section Area | mm² | mm², cm², m² |
Step by step
- 1. What you know: Resistivity (Ω·m) 1 × 10⁻⁶ Ω·m, Length 1 m, Cross-Section Area 10 mm²
- 2. The relation: R = ρ × L / A
- 3. Substitute: rho = 1 × 10⁻⁶ Ω·m, L = 1 m, A = 10 mm²
- 4. Result: Resistance = 100 mΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 100 mΩ | 2.8e-14% |
| E24 | 100 mΩ | 2.8e-14% |
Worked examples
Minimum range
Given: Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Length 1 mm, Cross-Section Area 0.1 mm²
Result: Resistance = 0.01 mΩ
Low range
Given: Resistivity (Ω·m) 1 × 10⁻⁸ Ω·m, Length 10 mm, Cross-Section Area 1 mm²
Result: Resistance = 0.1 mΩ
Typical
Given: Resistivity (Ω·m) 1 × 10⁻⁶ Ω·m, Length 1 m, Cross-Section Area 10 mm²
Result: Resistance = 100 mΩ
High range
Given: Resistivity (Ω·m) 0.001 Ω·m, Length 100 m, Cross-Section Area 1 cm²
Result: Resistance = 1 kΩ
Maximum range
Given: Resistivity (Ω·m) 0.01 Ω·m, Length 1 km, Cross-Section Area 10 cm²
Result: Resistance = 10 kΩ
Solving for each variable
Solve for Resistance
Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Length 1 mm, Cross-Section Area 0.1 mm² → 0.01 mΩ
Solve for Length
Resistance 1 Ω, Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Cross-Section Area 0.1 mm² → 100 m
Solve for Cross-Section Area
Resistance 1 Ω, Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Length 1 mm → 1 × 10⁻⁶ mm²
How Resistance changes with Resistivity (Ω·m)
| Resistivity (Ω·m) (input) | Resistance (result) |
|---|---|
| 1 × 10⁻⁷ Ω·m | 10 mΩ |
| 2.5 × 10⁻⁷ Ω·m | 25 mΩ |
| 5 × 10⁻⁷ Ω·m | 50 mΩ |
| 7.5 × 10⁻⁷ Ω·m | 75 mΩ |
| 1 × 10⁻⁶ Ω·m | 100 mΩ |
| 1.5 × 10⁻⁶ Ω·m | 150 mΩ |
| 2 × 10⁻⁶ Ω·m | 0.2 Ω |
| 4 × 10⁻⁶ Ω·m | 0.4 Ω |
| 7 × 10⁻⁶ Ω·m | 0.7 Ω |
| 1 × 10⁻⁵ Ω·m | 1 Ω |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 100 |
| Ω | 0.1 |
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<p><a href="https://vbatpower.com/formulas/wire-resistance/">Wire Resistance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Wire Resistance?
Use R = ρ × L / A. With Resistivity (Ω·m) 1 × 10⁻⁶ Ω·m, Length 1 m, Cross-Section Area 10 mm², Resistance works out to 100 mΩ.
What is the formula for Wire Resistance?
The formula is R = ρ × L / A. Wire resistance depends on the material's resistivity, the wire length, and its cross-sectional area.
How do you find Length when you know the other values?
Rearrange for Length: with Resistance 1 Ω, Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Cross-Section Area 0.1 mm², Length is 100 m.
How do you find Cross-Section Area when you know the other values?
Rearrange for Cross-Section Area: with Resistance 1 Ω, Resistivity (Ω·m) 1 × 10⁻⁹ Ω·m, Length 1 mm, Cross-Section Area is 1 × 10⁻⁶ mm².
What units does Wire Resistance use?
Resistance is shown in mΩ, Ω. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Wire & Cable formulas →Need more features?
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