Physics
Resistivity & resistance
Relate wire resistance, resistivity, length and area.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Resistance in ohms (Ω). | |
| Resistivity in ohm meters (Ω·m), at the stated temperature. | |
| Conductor length in meters. | |
| Cross-sectional area in m² and diameter in meters. |
Worked example
- Solve for
- Resistance R
- Resistivity ρ (Ω·m)
- 1.68e-8
- Wire length L
- 2
- Wire length unit
- m
- Cross-section input
- Circular wire diameter
- Wire diameter d
- 0.5
- Diameter unit
- mm
0.1711234 Ω
Follow the example steps
- 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
Common mistakes
Halve the diameter before calculating circular area.
Incorrect approach
d = 2 mm: A = π × 2² mm²
Correct approach
d = 2 mm, r = 1 mm: A = π × 1² mm² ≈ 3.142 mm²
More checks before you submit
- 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.
Method notes
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.