Physics
Resistivity & Wire Resistance Calculator
Solve R = ρL/A for any quantity. Use cross-sectional area directly, or enter the diameter of a circular wire.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
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Result & working
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Step-by-step working
The formula
R = ρL/A; ρ = RA/L; L = RA/ρ; A = ρL/R
For a circular wire: A = πd²/4
| Symbol | Meaning |
|---|---|
| R | Resistance in ohms (Ω). |
| ρ | Resistivity in ohm meters (Ω·m), at the stated temperature. |
| L | Conductor length in meters. |
| A, d | Cross-sectional area in m² and diameter in meters. |
When to use this calculator
Use this for a uniform conductor at a fixed temperature. Material resistivity depends on temperature and composition; enter the value appropriate to your experiment. The example value is illustrative, not a certified material reference.
Area units are squared: 1 mm² = 10⁻⁶ m². Doubling the diameter makes the circular area four times larger, so the ideal wire resistance becomes one quarter as large. All conversions are shown in the working.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- rho in SI = 1.68e-8 × 1 = 1.68e-8 Ω·m
- L in SI = 2 × 1 = 2 m
- d in SI = 0.5 × 0.001 = 0.0005 m
- A = πd²/4 = π × (0.0005)² / 4 = 1.963495e-7 m²
- R = ρL/A = 1.68e-8 × 2 / 1.963495e-7 = 0.1711234 Ω
0.1711234 Ω
Common mistakes
- Do not use a radius as though it were a diameter.
- Resistance Ω and resistivity Ω·m are different quantities.
- Contact and lead resistance can affect measured R.
- All four physical quantities must be positive in this uniform-conductor model.