What next?
Resistance is one term in Ohm’s law. These complete the circuit.
How to use this calculator
- Enter the material’s resistivity (ρ), or tap a preset.
- Enter the wire length in metres.
- Enter the cross-sectional area in mm².
What your result means
This is the DC resistance of a uniform conductor. Longer wires resist more; thicker wires resist less; and the material’s resistivity sets the baseline — copper and aluminium are low, which is why they are used for cabling.
Why this one is different
The square millimetres you type are converted to square metres inside the working, shown as the factor it is, because resistivity is quoted per metre and skipping that step is the classic million-fold error. Resistivity of 1.68×10⁻⁸ stays legible rather than rounding to zero, and the result appears in milliohms and kilohms beside ohms.
Double the thickness, quarter the resistance
Resistance falls in proportion to cross-sectional area, and area grows with the square of the radius. Doubling a wire’s diameter quadruples its area and cuts resistance to a quarter — the reason long-distance power cables are so thick.
How it works
Resistance equals resistivity times length divided by cross-sectional area. The calculator converts the area from mm² to m² automatically. Copper’s resistivity is about 1.68×10⁻⁸ Ω·m; aluminium’s is about 2.65×10⁻⁸ Ω·m.
Formula
Worked example
A 50 m run of copper cable with a 2.5 mm² cross-section (ρ = 1.68 × 10⁻⁸ Ω·m):
R = 1.68 × 10⁻⁸ × 50 ÷ 2.5 × 10⁻⁶
R = 0.336 Ω
At 20 A that resistance drops about 6.7 V and dissipates roughly 134 W as heat along the run — which is why long circuits need a larger cable size.
Resistance changes with temperature
The resistance of a conductor rises as it warms, and for copper it does so by roughly 0.4% per degree Celsius. Over a 50 °C rise that is a 20% increase — enough to matter for cable sizing, motor windings and any measurement made on a component that has been carrying current. Semiconductors and thermistors move the other way, falling with temperature, which is what makes them useful as sensors and dangerous in thermal runaway. Quote a resistance with the temperature it applies at whenever precision matters.
Series, parallel and where the current goes
Resistances in series add directly; in parallel the reciprocals add, so the combined value is always lower than the smallest branch. Two consequences are worth holding onto: adding any parallel path reduces total resistance and increases total current draw, and in a parallel network the lowest-resistance branch carries the most current. That is the mechanism behind both an overloaded circuit and a short — the fault path is simply a very low resistance in parallel with everything else.
Frequently asked questions
Why enter area in mm²?＋
Wire cross-sections are tiny, so mm² is the practical unit. The calculator converts to m² (×10⁻⁶) before applying the formula.
Does this include temperature effects?＋
No. Resistivity rises with temperature, so this gives the resistance at the reference temperature for the value you enter. Use a temperature-corrected resistivity for hot conductors.
Why do long cable runs need thicker cable?＋
Resistance rises in proportion to length, and every ohm costs you voltage at the far end. The 50 m copper run above has 0.336 Ω, which at 20 A drops 6.7 V and wastes about 134 W as heat. Going up one conductor size cuts the area penalty, because resistance falls as area rises.
What is resistivity and where do I find it?＋
It is the material property the calculation depends on, in ohm-metres. Copper is about 1.68 times ten to the minus eight, aluminium roughly 2.65, so aluminium needs a larger cross-section for the same resistance.
How much voltage drop is acceptable?＋
Wiring regulations typically limit it to a few percent of nominal supply voltage from origin to load, with tighter limits on lighting circuits than on power. Long runs are where this becomes the sizing constraint rather than current capacity.
Does resistance change with temperature?＋
Yes. Copper's resistance rises roughly 0.4 percent per degree Celsius, so a cable running hot in a bunched installation has meaningfully higher resistance than the cold value.
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Assumptions & limitations
Engineering formulas are exact; the situations they model are not. Read your result with these limits in mind:
- Resistivity values are quoted at 20 °C. Copper's resistivity rises about 0.39% per °C, so a hot cable resists noticeably more.
- Assumes a uniform cross-section along the whole length and a homogeneous conductor.
- DC only. At high frequency the skin effect pushes current to the conductor surface and the effective resistance rises.
- This is conductor resistance alone — it is not a cable-sizing calculation. Follow BS 7671 or your local wiring regulations for that.