Conductivity to Resistivity Calculator

Background.

Conductivity and resistivity describe one property from opposite ends. Conductivity, σ, says how readily a material carries current, in siemens per meter; resistivity, ρ, says how strongly it opposes current, in ohm-meters. Each is the reciprocal of the other, so converting between them is a single division: ρ = 1 ÷ σ.

Which of the two you meet depends on the trade. Wire tables and semiconductor data usually quote resistivity, often in microhm-centimeters or ohm-square-millimeters per meter. Water-quality meters, soil surveys and oceanographers usually report conductivity, often in microsiemens per centimeter. Copper anchors electrical engineering's own reference scale: the International Annealed Copper Standard sets 100% conductivity at 58 MS/m at 20 °C, a resistivity of 1.724 × 10⁻⁸ Ω·m.

The division is trivial; the units are where mistakes happen. This page works in SI throughout, siemens per meter in and ohm-meters out. A reading of 500 µS/cm from a water meter must first become 0.05 S/m, and a resistivity in Ω·cm is 100 times the Ω·m figure. One slipped prefix shifts the answer by a factor of a thousand or a million, and with numbers this large or this small the error is easy to miss.

Both quantities change with temperature, and the conversion assumes they describe the same sample under the same conditions. A metal's resistivity rises as it warms, while the conductivity of water climbs by around 2% per degree Celsius, which is why water meters usually report a value corrected to 25 °C. No temperature correction is applied here and no material value is assumed: you supply the conductivity, and the page returns its exact reciprocal.

What is conductivity to resistivity calculator?

Electrical resistivity is the resistance of a one-meter cube of a material measured between opposite faces, a property of the material itself rather than of any particular sample's size or shape. Its SI unit is the ohm-meter (Ω·m). Electrical conductivity is its reciprocal, measured in siemens per meter (S/m), a siemens being one reciprocal ohm. Converting conductivity to resistivity therefore means dividing 1 by the conductivity, with nothing else involved.

How to use this calculator.

1. 01Convert your conductivity to siemens per meter before entering it: multiply µS/cm by 0.0001, mS/cm by 0.1 and MS/m by 1,000,000. Copper at 100% IACS is 58,000,000 S/m.
2. 02Enter the value. Conductivities from 0.000058 S/m upward are accepted, so very pure water and electrical insulators fall outside the page's range.
3. 03Read the resistivity in ohm-meters. For Ω·cm multiply by 100, for µΩ·cm by 100,000,000, and for Ω·mm²/m by 1,000,000.
4. 04Keep a note of the temperature at which the conductivity was measured; the resistivity applies at that temperature only.

The formula.

ρ = 1 ÷ σ, where σ is the electrical conductivity in siemens per meter and ρ the resistivity in ohm-meters. The relationship is exact because the siemens is defined as the reciprocal of the ohm, which makes S/m and Ω·m reciprocal units by construction. No constants or material data enter the formula. Because it is a reciprocal, a tenfold rise in conductivity means a tenfold fall in resistivity, and very small conductivities produce very large resistivities. The number becomes useful in the next step: the resistance of a real conductor is R = ρL ÷ A, so resistivity multiplied by length and divided by cross-sectional area gives the ohms a wire, a circuit-board track or a column of liquid actually presents. The input must be a positive conductivity measured at a known temperature.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST Special Publication 811, Guide for the Use of the International System of Units.
2. [2]OpenStax, University Physics Volume 2, section 9.3, Resistivity and Resistance.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.