Calculate wire resistance, resistivity, length or cross-sectional area from any 3 values with metric and imperial unit options shown.
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Wire Resistance Formula
The wire resistance calculation is based on the relationship between resistance, resistivity, wire length, and cross-sectional area.
The same equation can be rearranged to solve for any missing value:
- R = resistance of the wire, in ohms (Ω)
- rho = resistivity of the wire material, in ohm-meters (Ω·m)
- L = wire length, in meters (m)
- A = cross-sectional area of the wire, in square meters (m²)
To use the calculator, enter any 3 values. The missing value is calculated from the matching rearranged formula. The calculator converts your selected units to base units first: Ω·m, meters, m², and Ω. It then converts the result back to the unit selected for the missing field.
Typical Resistivity Values for Common Wire Materials
Resistivity depends on the material and temperature. These values are typical at about 20°C.
| Material | Resistivity, Ω·m | Notes |
|---|---|---|
| Silver | 1.59 × 10-8 | Very low resistance |
| Copper | 1.68 × 10-8 | Common electrical conductor |
| Gold | 2.44 × 10-8 | Corrosion resistant |
| Aluminum | 2.82 × 10-8 | Lightweight conductor |
| Tungsten | 5.60 × 10-8 | Higher resistance than copper |
| Nichrome | 1.10 × 10-6 | Used for heating elements |
Unit Conversions Used in Wire Resistance Calculations
| Quantity | Conversion |
|---|---|
| Resistivity | 1 Ω·cm = 0.01 Ω·m |
| Length | 1 ft = 0.3048 m |
| Length | 1 in = 0.0254 m |
| Area | 1 cm² = 0.0001 m² |
| Area | 1 in² = 0.00064516 m² |
| Resistance | 1 kΩ = 1,000 Ω |
Example Calculations
Example 1: Calculate wire resistance
You have a copper wire with resistivity 1.68 × 10-8 Ω·m, length 10 m, and cross-sectional area 0.01 cm².
Convert area first:
Then calculate resistance:
The wire resistance is 0.168 Ω.
Example 2: Calculate wire length
A copper wire has resistance 2 Ω, resistivity 1.68 × 10-8 Ω·m, and cross-sectional area 0.01 cm².
Convert area first:
Then calculate length:
The wire length is about 119.05 m.
FAQ
Why does a longer wire have more resistance?
A longer wire gives electrons more material to pass through. This increases resistance. In the formula R = rho*L/A, resistance is directly proportional to length. If you double the wire length and keep the same material and area, the resistance doubles.
Why does a thicker wire have less resistance?
A thicker wire has a larger cross-sectional area. This gives current more space to flow. In the formula R = rho*L/A, resistance is inversely proportional to area. If the area doubles and the material and length stay the same, the resistance is cut in half.
Should you use one-way length or round-trip length?
Use the total conductor length that current travels through. For a single piece of wire, use that wire length. For a circuit with a supply wire and a return wire, use the combined round-trip conductor length if you want the total circuit resistance.