Resistor Calculators
Resistance of a Conductor Calculator
Work out the resistance of a length of wire or cable from its material, length and cross-sectional area.
Conductor Resistance
R = ρL ÷ A for wire, cable and strip.
The Resistivity Formula
The resistance of a uniform conductor depends on three things: what it is made of, how long it is, and how thick it is. Resistivity, written ρ and measured in ohm-metres, is the material property that captures the first of those.
Resistance rises in direct proportion to length and falls in inverse proportion to cross-sectional area. Doubling the length doubles the resistance; doubling the area halves it. Because area grows with the square of the diameter, doubling the diameter of a round conductor cuts its resistance to a quarter.
Resistivity itself changes with temperature, and for metals over a moderate range the change is close to linear:
| Material | ρ at 20 °C (Ω·m) | α (per K) |
|---|---|---|
| Silver | 1.586 × 10⁻⁸ | 0.00380 |
| Copper (annealed) | 1.724 × 10⁻⁸ | 0.00393 |
| Gold | 2.440 × 10⁻⁸ | 0.00340 |
| Aluminium | 2.826 × 10⁻⁸ | 0.00403 |
| Tungsten | 5.600 × 10⁻⁸ | 0.00450 |
| Iron | 9.710 × 10⁻⁸ | 0.00500 |
| Nichrome (80/20) | 1.100 × 10⁻⁶ | 0.00040 |
How to Use the Conductor Resistance Calculator
Choose the conductor material from the list. Each option carries its own documented resistivity and temperature coefficient, both shown in the table above so you can see exactly what the calculator is using.
Enter the length of the conductor and select a unit. Metres, kilometres, centimetres, feet and inches are all accepted and converted internally. Enter the cross-sectional area in square millimetres, square centimetres, square metres or kcmil.
Two optional fields extend the result. A temperature in degrees Celsius applies the linear correction above, which matters for conductors running warm. A current value adds the voltage drop across the conductor and the power it dissipates, using V = I × R and P = I² × R.
Worked Example: A Copper Cable Run
Take 25 metres of 1.5 mm² copper cable at room temperature.
That is the resistance of a single conductor. A two-wire circuit using this cable has roughly twice that, about 0.575 Ω, since the current has to return.
Carrying 10 A, the single conductor drops 2.87 V and dissipates 28.7 W. Raise the conductor temperature to 70 °C and the resistivity increases by about 19.7%, taking the resistance to roughly 0.344 Ω and the drop to 3.44 V. That temperature sensitivity is why cable calculations for loaded circuits are often done at the expected operating temperature rather than at 20 °C.
Reading Your Conductor Resistance Results
The conductor resistance is the value for one conductor of the length and area you entered. It is the number to use as a series resistance when analysing the circuit.
Resistance per metre is useful for scaling. Once you know a cable is 11.5 mΩ per metre, you can estimate any run length in your head without returning to the calculator.
The resistivity tile confirms which figure was applied, including any temperature correction, so the result is traceable rather than a black box. Where a current was supplied, the voltage drop and dissipation tiles show what that resistance costs you in delivered voltage and wasted heat.
Where Conductor Resistance Matters
Cable selection is the main one. Knowing the resistance per metre of a candidate cable lets you predict the drop before ordering, which matters for long runs, low-voltage lighting and battery systems where the supply voltage leaves little headroom.
The same formula designs heating elements. Nichrome is used precisely because its resistivity is roughly sixty times that of copper and changes very little with temperature, so a manageable length of wire produces a useful resistance and a predictable power output.
It also explains measurement error. Four-wire resistance measurement exists because the resistance of the test leads themselves, calculated exactly this way, becomes significant when measuring anything below about an ohm.
Circuit board design uses the same relationship. A copper track is simply a flat conductor, and its resistance follows R = ρL ÷ A with the area given by the track width multiplied by the copper thickness. Working that out is how designers decide how wide a power track needs to be, and it is why ground planes are used for return paths: an unusually large area gives an unusually small resistance.
Limits of the Resistivity Model
- The formula assumes a uniform cross-section and a homogeneous material. Stranded conductors have slightly more resistance than a solid conductor of the same nominal area, because of the helical lay of the strands.
- The temperature model is linear and reliable over a moderate range around room temperature. It becomes inaccurate at cryogenic temperatures and near a material's melting point.
- Only DC resistance is calculated. At high frequencies, skin effect confines current to the outer layer of the conductor and the effective resistance rises.
- Alloy compositions vary. Published resistivity for nichrome and similar alloys depends on the exact mix, so treat those figures as representative rather than exact.
Questions
Conductor Resistance FAQs
Does this give the resistance of the whole circuit?
No, it gives the resistance of one conductor. A two-wire circuit has both an outgoing and a returning conductor, so its loop resistance is roughly double this figure.
Why does aluminium need a larger cross-section than copper?
Its resistivity is about 64% higher, so for the same resistance an aluminium conductor needs a proportionally larger area. That is why aluminium feeders are typically sized up by around two AWG steps.
How much does temperature change the answer?
For copper, roughly 0.39% per degree above 20 °C. A conductor at 70 °C therefore has about 20% more resistance than the same conductor at room temperature.
Can I use this for a stranded cable?
Yes, using the nominal conductor area. The real value will be a little higher than calculated because the strands follow a helical path, making them slightly longer than the cable itself.
Feed the Resistance Into the Ohms Law Wheel
Open the full Ohms Law Wheel calculator to solve voltage, current, resistance and power from any two known values.