What this calculator does
The resistance of a straight length of wire depends on three things: what it is made of, how long it is, and how thick it is. A wire resistance calculator combines these using R = (resistivity x length) / cross-sectional area, the same relationship used to size cables, wind heating elements and work out voltage drop over a long run.
The material matters more than people expect. Copper and silver are excellent conductors with very low resistivity, aluminium is a common cheaper alternative with noticeably more resistance for the same size, and nichrome is chosen deliberately for the opposite reason: its high resistivity is what makes it heat up in toasters and heating elements rather than simply carrying current efficiently.
The formula
Resistivity (the Greek letter rho) is a property of the material, in ohm-metres. Multiplying it by the wire length and dividing by the cross-sectional area (worked out from the diameter you enter) gives the total resistance in ohms. A longer or thinner wire always has more resistance; a shorter or thicker one always has less.
| Term | Meaning |
|---|---|
| R | Resistance of the wire, in ohms. |
| rho | Resistivity of the material, in ohm-metres, a fixed property of copper, aluminium and so on. |
| Length | The total length of wire the current travels through. |
| Area | Cross-sectional area of the wire, calculated from its diameter. |
The inputs explained
| Field | What to enter |
|---|---|
| Wire material | Pick a common conductor for its standard resistivity, or choose Custom to enter your own. |
| Resistivity (used only when material is Custom), ohm.m | Only used when Material is set to Custom. Ignored otherwise. |
| Wire length (m) | The total length of wire in the circuit, not the straight-line distance between two points if the run is coiled or routed. |
| Wire diameter (mm) | The bare conductor diameter, not including any insulation. |
When to use it
Estimating voltage drop on a long cable run
Multiplying the calculated resistance by the expected current (using Ohm's law, V = IR) gives the voltage lost along the cable, which matters for long solar, automotive or outbuilding runs.
Checking a heating element
Nichrome wire is chosen for its resistivity. Working out the resistance of a coil of a given length and gauge tells you the current and power it will draw at a given voltage before it is wound.
Comparing copper and aluminium for the same job
Aluminium wire needs a larger diameter than copper to reach the same resistance, which is why aluminium cable is usually sized up compared with an equivalent copper run.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does wire diameter change the resistance of a 10 m copper wire?
The same 10 m length of copper, at a range of wire diameters.
| Diameter | Resistance | Resistance per metre |
|---|---|---|
| 0.50 mm | 0.8556 ohm | 0.085562 ohm/m |
| 1.00 mm | 0.2139 ohm | 0.021390 ohm/m |
| 1.50 mm | 0.0951 ohm | 0.009507 ohm/m |
| 2.05 mm | 0.0509 ohm | 0.005090 ohm/m |
| 3.00 mm | 0.0238 ohm | 0.002377 ohm/m |
| 5.00 mm | 0.0086 ohm | 0.000856 ohm/m |
How does resistance compare across common wire materials?
The same length and diameter of wire, in five common materials.
| Material | Resistance | Resistivity used |
|---|---|---|
| Copper | 0.0509 ohm | 1.680e-8 ohm.m |
| Aluminium | 0.0854 ohm | 2.820e-8 ohm.m |
| Silver | 0.0482 ohm | 1.590e-8 ohm.m |
| Gold | 0.0739 ohm | 2.440e-8 ohm.m |
| Nichrome | 3.333 ohm | 1.100e-6 ohm.m |
Questions
What is the difference between this and a wire gauge calculator?
A wire gauge (AWG) calculator converts a gauge number to a physical diameter and area. This calculator takes that diameter (or one you measure directly) and works out the actual resistance of a specific length of wire made from a specific material.
Why does aluminium wire need to be thicker than copper?
Aluminium has roughly 1.6 times the resistivity of copper. To match copper's resistance for the same length, an aluminium conductor needs a larger cross-sectional area, which is why aluminium cable is typically rated at a larger gauge for the same job.
Does temperature affect wire resistance?
Yes. Resistivity rises with temperature for metals, so a wire running hot has somewhat higher resistance than the same wire at room temperature. This calculator uses standard resistivity figures at room temperature and does not adjust for operating temperature.
How do I find the resistivity of a material not listed here?
Select Custom and enter the resistivity in ohm-metres from a materials reference or datasheet. Values are typically quoted at 20 degrees Celsius unless stated otherwise.
To convert an AWG size to its diameter and area first, see the Wire Gauge Calculator. To size a cable from a current and acceptable voltage drop instead, see the Wire Size Calculator.