Resistivity Calculator
Find resistivity from resistance, length and area, or resistivity from temperature. Copper ρ≈1.68e-8 Ω·m; L=1 m, A=1e-6, R≈0.0168 Ω.
Input Data
Results
At a glance:Resistivity ρ is a material property defined by R=ρL/A (R resistance, L length, A cross-section), in ohm-metres (Ω·m). Conductivity σ=1/ρ. The temperature dependence is ρ(T)=ρ0[1+α(T−T0)], where α is the temperature coefficient. Properties: (1) metals have low resistivity (copper ~1.68e-8 Ω·m); (2) insulators have very high resistivity (rubber ~1e13 Ω·m); (3) semiconductors lie in between and vary strongly with temperature and doping. Applications: (1) cable and wire sizing; (2) material grading and quality control; (3) RTD temperature sensors; (4) PCB trace design; (5) grounding and earthing systems.
Formula
Resistivity: ρ = R·A/L
Temperature: ρ(T) = ρ₀[1+α(T−T₀)]
Conductivity: σ = 1/ρ
$$\rho = \frac{R A}{L}, \quad \rho(T) = \rho_0\left[1 + \alpha (T - T_0)\right]$$How to Use
- Enter resistance R, length L and area A to get resistivity ρ.
- Or use the temperature mode: enter ρ₀, α and temperature T.
- The result is in ohm-metres (Ω·m).
Case Studies
Selecting copper versus aluminum wiring
Copper ρ=1.68e-8 Ω·m, aluminum ρ=2.65e-8 Ω·m. For the same resistance, aluminum needs a larger cross-section.
Aluminum is lighter and cheaper, used in overhead power lines; copper is preferred for building wiring in Hong Kong.
A 1 m, 1 mm² copper wire has R≈0.0168 Ω; aluminum the same size ≈0.0265 Ω.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.