Wire Resistance Calculator
Find a wire's resistance from material, length and cross-section.
A wire's resistance grows with length and shrinks with thickness.
How the Math Works
The Wire Resistance Calculator uses the fundamental equation R = ρ·L ÷ A to determine electrical resistance. Here, resistivity (ρ) is a material-specific constant measured in ohm-meters (Ω·m), length (L) is the conductor's physical length in meters, and cross-sectional area (A) is the wire's thickness in square meters. The formula shows resistance increases linearly with length and decreases with larger cross-sectional areas. For example, doubling a copper wire's length doubles its resistance, while doubling its thickness reduces resistance by half. This relationship allows precise calculations for any conductor material, from copper to aluminum, ensuring accurate resistance predictions based on physical dimensions.
Practical Applications
This calculator is essential for electrical engineers designing circuits, electricians selecting appropriate wire gauges, and DIY enthusiasts building projects safely. By inputting material resistivity (e.g., copper at 1.68×10⁻⁸ Ω·m), wire length, and diameter, users instantly determine resistance to prevent overheating, voltage drops, or fire hazards. It ensures compliance with electrical codes, optimizes power efficiency in appliances, and helps choose cost-effective wire sizes—thicker wires reduce resistance for high-current applications like home wiring, while thinner wires suffice for low-power electronics. This tool eliminates manual calculations, saving time during system design or troubleshooting.
Day-to-Day Use
Understanding wire resistance helps explain everyday electrical phenomena, from why thick power cords are used for high-wattage devices to why extension cords can overheat when overloaded. It informs safer choices, like replacing frayed appliance cords or selecting adequate wiring for home renovations to prevent circuit breaker trips. For instance, knowing that a 100-foot aluminum wire has higher resistance than a copper one of the same size explains why aluminum wiring requires larger gauges in homes. This knowledge empowers users to make informed decisions about device usage, energy efficiency, and electrical safety in daily life.
Worked example
50 m of 2.5 mm² copper → about 0.34 Ω.
FAQ
Why does long thin wire heat up?
Higher resistance dissipates more power (P = I²R) for the same current.