Wire Resistance Calculator
Copper wire ohms from length and diameter with weight.
What it does
Copper wire resists by length over area. A hundred meters of two millimeter diameter runs about half an ohm. Doubling length doubles ohms, doubling diameter quarters them.
The tool above takes length and diameter and returns resistance, conductance, and copper weight. The defaults 100 m with 2 mm match the worked example, so the page opens showing 0.535 ohm. Switch to imperial for feet and mils.
Resistance is rho times length over pi times radius squared with rho 1.68e-8 ohm meters at 20 C. Conductance inverts. Weight multiplies volume by 8960 kg/m3. Here area 3.14 square mm gives 0.535 ohm and 2.81 kg.
Use this for voltage drop budgets and heating estimates. Stranded fill, temperature rise, and skin effect at high frequency shift real values. Aluminum needs its own rho.
This page shows the formula, one full hand checked example at 100 m, a reference table, and practice checks that run through the tool in both unit systems.
How to use
- Pick Metric (m, mm) or Imperial (ft, mil).
- Type wire length one way.
- Type diameter (mil is 0.001 in).
- Read Resistance in ohms.
- Read Conductance in siemens.
- Double run for there and back loops.
Formula
- rho
- 1.68e-8 ohm m copper at 20 C.
- L
- One way length in meters.
- A
- Cross section in square meters.
Feet convert at 0.3048 m, mils at 0.0254 mm. Solid round assumed. Temperature coefficient outside.
Worked example
Example: 100 m, 2 mm copper
Find resistance of 100 meters with 2 mm diameter.
- Radius: 2 / 2 = 1 mm = 0.001 m.
- Area: pi x 0.001 squared = 0.0000031416 m2.
- Numerator: 1.68e-8 x 100 = 0.00000168.
- Divide: 0.00000168 / 0.0000031416 = 0.535 ohm.
- Conductance: 1 / 0.535 = 1.87 S.
- Weight: 8960 x 100 x area = 2.81 kg.
Reference table
| Diameter | Area | Ohms |
|---|---|---|
| 1 mm | 0.785 mm2 | 2.139 ohm |
| 2 mm | 3.142 mm2 | 0.535 ohm |
| 4 mm | 12.566 mm2 | 0.134 ohm |
Limits
- Copper at 20 C only.
- Solid round assumed. Stranded fill differs.
- DC form. Skin effect ignored.
- One way length. Loops double.
Common mistakes
- Using diameter as radius, off by 4 times.
- Mixing mm with meters in area.
- Forgetting there and back doubles length.
- Applying copper rho to aluminum.
- Reading mils as mm.
Try it yourself
Quick checks. Answers sit tucked under each question.
10 m, 1 mm?
Resistance 0.214 ohm, conductance 4.675 S.
100 m, 2 mm weight?
2.81 kg copper.
Questions
100 m 2 mm?
0.535 ohm.
Thicker?
Area squares, so double diameter quarters ohms.
Longer?
Linear. Double length doubles ohms.
Aluminum?
Needs 2.82e-8 rho, not here.
Loop?
Double one way length.
Mil?
0.001 in. Here 79 mil near 2 mm.