Wire Resistance Calculator
Calculate the electrical resistance of wire based on gauge, length, material, and temperature. Essential for accurate voltage drop and power loss calculations.
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What is Wire Resistance?
Wire resistance is the opposition to the flow of electric current through a conductor. All wires have some resistance, which causes voltage drop and power loss when current flows. Understanding wire resistance is crucial for proper electrical system design.
Why Calculate Wire Resistance?
Calculating wire resistance helps you:
- Predict voltage drop in long wire runs
- Calculate power losses and heat generation
- Size wire properly for sensitive equipment
- Design efficient electrical systems
- Troubleshoot electrical problems
Wire Resistance Formula
The resistance of a wire is calculated using:
R = ρ × L / A
Where:
- R = Resistance (Ohms)
- ρ = Resistivity of material (Ohm-meters)
- L = Length of wire (meters)
- A = Cross-sectional area (square meters)
Factors Affecting Wire Resistance
1. Wire Length
Resistance increases proportionally with length. Doubling the wire length doubles the resistance.
2. Wire Gauge (Cross-Sectional Area)
Resistance decreases with larger wire diameter. A 10 AWG wire has approximately one-fourth the resistance of 14 AWG wire.
3. Material Type
Different materials have different resistivity:
- Copper: 1.724 × 10⁻⁸ Ω·m (at 20°C)
- Aluminum: 2.825 × 10⁻⁸ Ω·m (at 20°C) - about 64% higher than copper
- Silver: 1.59 × 10⁻⁸ Ω·m (lowest but expensive)
4. Temperature
Resistance increases with temperature. For copper, resistance increases approximately 0.4% per °C. The temperature-adjusted resistance formula:
R₂ = R₁ × [1 + α(T₂ - T₁)]
Where α is the temperature coefficient (0.00393 for copper at 20°C)
Wire Resistance Table (Copper at 20°C)
| AWG | Diameter (mm) | Ω/1000ft | Ω/km |
|---|---|---|---|
| 14 | 1.628 | 2.525 | 8.282 |
| 12 | 2.053 | 1.588 | 5.211 |
| 10 | 2.588 | 0.999 | 3.277 |
| 8 | 3.264 | 0.628 | 2.061 |
| 6 | 4.115 | 0.395 | 1.296 |
| 4 | 5.189 | 0.249 | 0.815 |
| 2 | 6.544 | 0.156 | 0.512 |
Practical Applications
Voltage Drop Calculation
Wire resistance is the key factor in voltage drop. For a given current I:
Voltage Drop = I × R × 2
(Multiply by 2 for round-trip resistance in DC circuits)
Power Loss
Power dissipated as heat in the wire:
Power Loss = I² × R
Temperature Rise
Higher resistance means more heat generation. Proper wire sizing ensures the wire doesn't overheat under load.
Example Calculation
Example: 100-foot run of 12 AWG copper wire
- Wire resistance: 1.588 Ω per 1000 ft
- 100-foot resistance: 1.588 × (100/1000) = 0.1588 Ω
- Round-trip resistance: 0.1588 × 2 = 0.3176 Ω
- At 20A load: Voltage drop = 20A × 0.3176Ω = 6.35V
- Power loss: 20² × 0.3176 = 127 watts
Tips for Minimizing Resistance
- Use larger wire gauge (lower AWG number) for long runs
- Minimize wire length when possible
- Use copper instead of aluminum for lower resistance
- Keep connections clean and tight to avoid contact resistance
- Consider wire operating temperature in calculations
Related Tools
For complete electrical calculations, check out:
- Voltage Drop Calculator - Calculate voltage loss
- Wire Gauge Calculator - Size wire properly
- AWG Chart - Complete wire specifications