Circuits and conductors
Resistance and resistivity
- where
- resistance (Ω)
- resistivity at operating temperature (Ω·m)
- conductor length (m)
- cross-sectional area (m²)
Explain this equation
Works out a conductor’s resistance from its material, length and cross-sectional area. Used for voltage drop and loop resistance estimates.
R is resistance in ohms. ρ (rho) is the material’s resistivity at its operating temperature: about 1.72 × 10⁻⁸ Ω·m for copper at 20 °C. l is the length of conductor and A is its cross-sectional area.
Resistance rises with length because charge has further to travel through the material. It falls with area because a bigger section gives more parallel paths. ρ sets how good the material is at conducting.
Sense check: 10 m of 2.5 mm² copper is about 0.069 Ω. Double the length and R doubles; double the area and R halves.
Watch out: for a circuit loop, count both line and return conductors. Units must match ρ: Ω·m with m², or Ω·mm²/m with mm².
Longer conductors have more resistance; greater cross-sectional area gives less resistance. Material and temperature affect resistivity.
For a two-wire circuit, distinguish one conductor’s length from the full outgoing-and-return loop. This formula is not by itself a cable current-rating method.
Enter your values to see the result.
Common mistake
Forgetting the return conductor when finding loop resistance.
Limits
Uniform material/area and stated temperature; dimensions must match ρ.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.