Conductivity to Resistivity Calculator - Sigma, Rho, and Temperature

A conductivity to resistivity calculator converts an electrical conductivity value (σ, in S/m) into the matching resistivity (ρ, in Ω·m) using ρ = 1/σ. It also reads the reverse direction, so a resistivity value in Ω·m gives the conductivity in S/m. The same form scales both sides to the operating temperature using a linear α correction.

• • Cross-checking a tabulated metal value: Confirm the conductivity of copper (≈ 5.80 × 10⁷ S/m at 20 °C) and the matching 1.724 × 10⁻⁸ Ω·m resistivity without redoing the inversion by hand.
• • Comparing electrolytes at 20 °C: Convert a seawater conductivity (5 S/m) or a distilled water value (5.5 × 10⁻⁶ S/m) into the matching resistivity so electrode and membrane specs read in the same unit.
• • Working a multi-step physics problem: Use ρ = 1/σ as the standalone step that links a measured conductance to the material's resistivity, then feed ρ into a length-and-area resistance calculation.

Conductivity and resistivity describe the same material property from opposite directions. Conductivity says how well the material carries current; resistivity says how strongly it resists. The two are tied by ρ = 1/σ, the same form that connects conductance G and resistance R. According to the Engineering Toolbox, copper sits at 5.80 × 10⁷ S/m and 1.724 × 10⁻⁸ Ω·m at 20 °C, the pair the copper preset starts from.

The two are tied together by the reciprocal relation ρ = 1/σ, which is the same form that connects the conductance G and the resistance R of a circuit element, and the ohm's law calculator covers the V/I/R relationship that sits behind that definition.

The conductivity to resistivity calculator uses the textbook reciprocal relation, then folds in a linear temperature correction so the result matches the operating point. The same two numbers back the secondary readouts.

• σ: Electrical conductivity in siemens per metre (S/m). The SI unit for how well a material carries current.
• ρ: Electrical resistivity in ohm-metres (Ω·m). The SI unit for how strongly a material resists current flow.
• α: Linear temperature coefficient of conductivity (1/°C) at the 20 °C reference. Copper 0.00393 1/°C; aluminum 0.00403 1/°C; silver 0.0038 1/°C.
• T: Operating temperature in °C. The 20 °C reference is the standard baseline used by the NIST and Engineering Toolbox tables.

The same form works in reverse. Entering a resistivity value (for example, 0.2 Ω·m for seawater) gives the matching conductivity (5 S/m) with no extra step, because the calculator treats whichever value you typed as the source and computes the other from it. The temperature correction always rescales the conductivity by 1 / (1 + α × (T − 20 °C)), so a hotter metal looks slightly less conductive at the same time.

According to Engineering Toolbox conductivity and resistivity reference, copper has a conductivity of 5.80 × 10⁷ S/m and a resistivity of 1.724 × 10⁻⁸ Ω·m at 20 °C, and silver has the lowest resistivity in the table at 1.59 × 10⁻⁸ Ω·m.

Four small ideas cover every number the calculator returns.

The reciprocal relation only works cleanly when the temperature is the same on both sides. Mixing a 20 °C conductivity with a 90 °C resistivity gives a misleading pair, so the calculator scales the same input through the same α in one step. For aqueous electrolytes, the temperature coefficient is not a constant: seawater at 25 °C sits closer to 6 S/m than 5 S/m, so the linear α is a usable approximation.

The reciprocal relation only works cleanly when the temperature is the same on both sides, and the heat transfer conduction calculator handles the analogous thermal conductivity with the same one-over-x form for heat flow.

Five short steps take a tabulated number to a temperature-corrected reciprocal value.

1. 1 Pick the material preset: Choose Copper for the standard 5.80 × 10⁷ S/m reference value, or pick Aluminum, Silver, Gold, Seawater, or Distilled water. Custom clears the preset for your own values.
2. 2 Enter the starting value: Type the conductivity in S/m (typical metals use scientific notation: 5.8e7) OR the resistivity in Ω·m. Whichever field you fill is the source.
3. 3 Set the operating temperature: Use the actual operating temperature in °C, not the room temperature. A board inside an enclosure easily sits at 60 °C, growing the resistivity by roughly 16 % for copper.
4. 4 Adjust the temperature coefficient if needed: Stay on the preset value for published metals. Switch to Custom and enter your own α (1/°C) for alloys, semiconductors, or liquids where the linear approximation is not accurate enough.
5. 5 Read the result panel: The result panel shows the conductivity, the resistivity, the conductance normalised to a 1 m run, and the resistance of a 1 m × 1 m × 1 m cube. All four numbers use the same temperature scaling and the same α.

For an aluminum busbar at 35 °C, choose the Aluminum preset, leave the conductivity at 3.5 × 10⁷ S/m, set the temperature to 35, and read the resistivity in Ω·m. The panel will report roughly 3.00 × 10⁻⁸ Ω·m. To turn that into a resistance for the actual busbar geometry, feed the resistivity and the cross-section into the cross-sectional area calculator, which handles the length and area that this calculator does not ask for.

To turn that into a resistance for the actual busbar geometry, feed the resistivity and the cross-section into the cross-sectional area calculator, which handles the length and area that this calculator does not ask for.

A purpose-built calculator keeps the unit pair, the temperature, and the material preset in one place so the inversion stays consistent.

• • Bidirectional in one form: The same form accepts either conductivity (S/m) or resistivity (Ω·m) as the source and returns the matching partner value.
• • Temperature-corrected by default: The operating temperature feeds a linear α correction, so the result reflects the real operating point instead of a 20 °C tabulated value. The same correction applies to both directions.
• • Material presets with safe overrides: Copper, aluminum, silver, gold, seawater, and distilled water are exposed as one-click presets. Custom clears the preset for unusual alloys or measured liquids.
• • Secondary readouts in SI units: The result panel adds the conductance per metre and the resistance of a 1 m cube, both in SI units, so the converted value lines up with the rest of a circuit calculation.
• • Wide range handling: Conductivities from 10⁻⁶ S/m (distilled water) to 10⁸ S/m (silver) read in scientific notation without overflow.

When the conductivity has to feed a wire-size or trace-width calculation, the resistivity is the property to read off. Take that value together with the conductor length into the cross-sectional area calculator to get a resistance in ohms, and the inverse gives a conductance that drops into the same V = I × R step. The form also covers the load-and-source pair a typical divider needs: feed the converted resistance into the voltage divider calculator and the result panel reports the node voltages at each tap without re-entering the unit pair.

Three variables drive the conversion, and two limitations tell you when the linear model stops being accurate.

• • The linear α correction is accurate for metals across the practical engineering range but underestimates the change at very low or very high temperatures.
• • The material presets are 20 °C reference values. Aqueous electrolytes do not follow a fixed α, so the temperature correction is an approximation for seawater and distilled water.

For seawater and other ionic solutions, the conductivity also depends on salinity and on the ion mix, which the linear α correction does not capture.

According to BIPM SI Brochure (9th edition), the siemens is the SI unit of conductance and the reciprocal of the ohm, which is why the calculator's primary unit pair is S/m for conductivity and Ω·m for resistivity.

According to Wikipedia electrical resistivity and conductivity reference, the SI unit of electrical conductivity is the siemens per metre (S/m), the SI unit of electrical resistivity is the ohm-metre (Ω·m), and the two are tied by σ = 1/ρ at the same temperature.

Once the resistance is known, the thermal side of the same I²R dissipation runs through the specific heat calculator, which handles the energy budget once the joule-heating is already on paper.