Wire Resistance Calculator
Find a wire's resistance from length and area.
Copper ≈ 1.68e-8
Results update as you type.
How it works
The electrical resistance of a wire depends on its material, length, and thickness, and this calculator computes it. You enter the wire length, the cross-sectional area, and the material's resistivity, and it returns the resistance in ohms and the resistance per kilometer. The formula is resistance equals resistivity times length divided by area. Each factor is intuitive: a longer wire has proportionally more resistance because current fights friction over a greater distance, a thicker wire (larger cross-section) has less resistance because current has more room to flow, and the resistivity captures how strongly the material itself opposes current. Copper, the most common conductor, has a low resistivity of about 1.68 times ten to the minus eight ohm-meters, aluminum is a bit higher but lighter and cheaper, and materials like nichrome have much higher resistivity, which is why they are used in heating elements. This calculation matters for electrical design: excessive wire resistance causes voltage drop and power loss as heat, so engineers choose a wire gauge thick enough to keep resistance low over the run length, especially for long cables or high currents. The calculator uses area in square millimeters and converts internally, with resistivity defaulting to copper. For accurate results, use the resistivity of your actual conductor and note that resistance also rises slightly with temperature. Enter the length, area, and resistivity to find the wire resistance.
R = ρ × L / A
A conductor's resistance equals its material resistivity times its length divided by its cross-sectional area. Longer wires have more resistance, while thicker wires have less. Resistivity is an intrinsic material property; copper is about 1.68 × 10⁻⁸ ohm-meters, and aluminum is somewhat higher, making copper the preferred conductor for most wiring.
Source:Electrical engineering
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter wire length and cross-sectional area.
- 2
Adjust the options
Adjust resistivity if they apply — sensible defaults are already set.
- 3
Read your result
Wire resistance updates instantly as you type — no button to press.
Frequently asked questions
How do you calculate wire resistance?
Multiply the material's resistivity by the wire length, then divide by the cross-sectional area. With resistivity in ohm-meters, length in meters, and area in square meters, the result is in ohms. The calculator accepts area in square millimeters and converts it, defaulting the resistivity to copper's value.
Why does a longer wire have more resistance?
Resistance is proportional to length because the current must travel through more material, encountering more opposition along the way. Doubling the length doubles the resistance. This is why long cable runs can suffer significant voltage drop, and why keeping conductors as short as practical helps minimize resistance and power loss.
Why does a thicker wire have less resistance?
Resistance is inversely proportional to cross-sectional area, so a thicker wire gives the current more parallel paths to flow through, reducing resistance. Doubling the area halves the resistance. This is why heavy loads and long runs use thicker gauge wire, to keep resistance, voltage drop, and heating within safe limits.
What is resistivity?
Resistivity is an intrinsic property of a material describing how strongly it opposes electric current, in ohm-meters. Good conductors like copper (about 1.68 times ten to the minus eight) and silver have low resistivity; aluminum is a bit higher; and resistive alloys like nichrome are much higher, making them useful for heating elements. It sets the baseline for a wire's resistance.
Does temperature affect wire resistance?
Yes. For metals, resistance increases with temperature, since higher temperatures cause more atomic vibration that impedes electron flow. This calculator uses the resistivity at a reference temperature, typically around 20 degrees Celsius. For precise work at other temperatures, adjust the resistivity using the material's temperature coefficient of resistance.