Free Conductivity to Resistivity Calculator

Electrical Resistivity and Conductivity: The Inverse Relationship

This free online conductivity to resistivity converter functions as an electrical conductivity calculator and a resistivity calculator, enabling you to quickly derive resistivity from conductivity or reverse the conversion with a single input.

What Are Resistivity and Conductivity?

Electrical resistivity (symbol $\rho$) quantifies how strongly a material opposes the flow of electric current. Electrical conductivity (symbol $\sigma$) measures a material’s ability to conduct electricity. These are intrinsic material properties—they depend only on the charge carrier density and temperature of the substance, not on the dimensions of the sample. Metals such as silver and copper have high conductivity and correspondingly low resistivity, while insulators like rubber and glass exhibit extremely high resistivity and low conductivity.

The Inverse Relationship

Resistivity and conductivity are reciprocals of each other. The mathematical relationship is straightforward:

$$\rho = \frac{1}{\sigma} \quad \text{and} \quad \sigma = \frac{1}{\rho}.$$

Therefore, if you know the conductivity of a material, its resistivity is simply the reciprocal of that value, and vice versa.

Worked Examples

Silver: Silver has an electrical conductivity of $6.29 \times 10^{7}\ {(\Omega\cdot\text{m})}^{-1}$. Using the reciprocal relation, its resistivity is:

$$\rho_{\text{silver}} = \frac{1}{6.29 \times 10^{7}} \approx 1.59 \times 10^{-8}\ \Omega\cdot\text{m}.$$

Copper: The resistivity of copper is $1.68 \times 10^{-8}\ \Omega\cdot\text{m}$. Taking the reciprocal gives its conductivity:

$$\sigma_{\text{copper}} = \frac{1}{1.68 \times 10^{-8}} \approx 5.95 \times 10^{7}\ {(\Omega\cdot\text{m})}^{-1} \text{ or } 5.95 \times 10^{7}\ \text{S/m}.$$

These examples demonstrate how this conductivity to resistivity solver handles the calculations instantly.

How to Use the Calculator

Using this resistivity from conductivity tool is simple:

1. Choose a material from the drop‑down menu (silver, copper, aluminum, etc.) or manually enter a custom conductivity value.
2. The tool automatically displays the corresponding resistivity.
3. To convert in the opposite direction, input a resistivity value, and the converter will calculate the conductivity.

This two‑way functionality makes it a versatile conductivity converter that serves both as a resistivity calculator and an electrical conductivity calculator for a wide range of applications.

Units of Measurement

The SI unit of resistivity is the ohm‑meter ($\Omega\cdot\text{m}$). Since conductivity is the reciprocal, its SI unit is ${(\Omega\cdot\text{m})}^{-1}$, which is also called siemens per meter ($\text{S/m}$). Both forms are used interchangeably in science and engineering.

Important Notes on Resistivity

It is essential to remember that resistivity is an intrinsic property: it depends solely on the material’s composition and temperature, not on its length, area, or shape. For instance, a wire with a resistivity of $10\ \Omega\cdot\text{m}$ will retain that same resistivity even if it is stretched to twice its original length. (The overall resistance of the wire changes with its dimensions, but the material’s resistivity—a fundamental property—remains constant.)