Calculates a wire’s electrical resistance from its material’s resistivity, its length, and its cross-sectional area.
How it works
Resistivity is multiplied by wire length and divided by cross-sectional area.
What this does not include
This does not include temperature effects — resistivity changes somewhat with temperature, and this calculator uses a fixed value at a reference temperature (20°C for the copper default).
How to use this calculator
- Enter the material’s resistivity (copper’s value is pre-filled), the wire length, and its cross-sectional area.
A worked example
A copper wire (resistivity 1.68×10⁻⁸ Ω·m), 10 m long, 1 mm² cross-section: resistance = ρL/A = 0.168 Ω.
The same copper, 100 m long, 0.5 mm² cross-section: resistance = 3.36 Ω — both a longer run and a thinner wire push resistance up.
What the variables mean
| Variable | Meaning |
|---|---|
| Resistivity | Material property — how strongly a material resists current flow |
| Length | Wire length |
| Cross-sectional area | Wire’s thickness, as a cross-section area |
Edge cases worth knowing
Resistance rises with length but falls with cross-sectional area — a longer wire has more resistance, a thicker one has less, which is why undersized wiring on long runs is a real electrical hazard.
A cross-sectional area of zero makes resistance infinite, which has no physical meaning, so the calculator declines to show a result.
Frequently asked questions
Why does a longer wire have more resistance?
A longer path means electrons encounter more material to collide with and lose energy to, directly increasing resistance in proportion to length.
Why does a thicker wire have less resistance?
A larger cross-sectional area gives electrons more parallel paths to flow through, reducing overall resistance — resistance is inversely proportional to area.
How do I convert wire gauge to cross-sectional area?
Standard wire gauge tables list the cross-sectional area for each gauge size — look up the specific gauge to get the area needed for this calculator.
