What the resistivity calculator does
This calculator finds the electrical resistivity (ρ, "rho") of a material from a real measurement: the resistance of a uniform sample, its length, and its cross-sectional area. Resistivity is an intrinsic property of a material — unlike resistance, it does not depend on the size or shape of the piece, so it is the number you use to compare copper with aluminium, or to identify an unknown conductor. The tool also reports the material's conductivity (σ), which is simply the reciprocal of resistivity.
How to use it
Enter three measured values and read the result:
- Resistance R — the total resistance of the sample in ohms (Ω), for example from a four-wire (Kelvin) measurement.
- Length L — the distance the current travels along the sample, in metres.
- Cross-sectional area A — the area the current flows through, in square metres. For a round wire of diameter d, A = π × (d / 2)2. Remember that 1 mm² equals 0.000001 m².
The main output is resistivity in ohm-metres (Ω·m). The table also gives it in micro-ohm-metres (μΩ·m), which is numerically identical to the common engineering unit Ω·mm²/m, plus the conductivity in siemens per metre.
The formula explained
Resistance, resistivity, length, and area are linked by the definition of resistivity. Starting from the resistance of a uniform conductor and solving for ρ:
$$ R = \rho \frac{L}{A} \quad\Rightarrow\quad \rho = \frac{R \cdot A}{L} $$Conductivity is the reciprocal of resistivity:
$$ \sigma = \frac{1}{\rho} $$Here R is in ohms, L in metres and A in square metres, giving ρ in ohm-metres (Ω·m) and σ in siemens per metre (S/m). The formula assumes a uniform sample at a fixed temperature, because resistivity rises with temperature for most metals.
Worked example
A copper wire is 10 m long with a cross-sectional area of 0.000001 m² (1 mm²), and its measured resistance is 0.168 Ω. Substituting into the formula:
$$ \rho = \frac{0.168 \times 0.000001}{10} = 1.68 \times 10^{-8}\ \Omega\cdot\text{m} $$The conductivity is the reciprocal:
$$ \sigma = \frac{1}{\rho} = 5.95 \times 10^7\ \text{S/m} $$A resistivity of 1.68 × 10-8 Ω·m (0.0168 μΩ·m) matches the textbook value for annealed copper at 20 °C, confirming the sample is copper.
Frequently asked questions
What is the difference between resistivity and resistance? Resistance (R, in ohms) depends on the size and shape of a specific object, while resistivity (ρ, in ohm-metres) is an intrinsic property of the material itself. A long thin wire and a short fat wire of the same metal have different resistances but identical resistivity.
How do I get the cross-sectional area of a round wire? Use A = π × (d / 2)2, where d is the wire diameter. For example, a 2 mm diameter wire has A = π × (0.001)2 ≈ 0.00000314 m². Convert from mm² to m² by multiplying by 0.000001.
Does temperature affect the result? Yes. Resistivity of most metals increases with temperature, so published reference values are quoted at a specific temperature, usually 20 °C. Measure resistance at a known temperature if you want to compare your result against reference tables.
