Conductivity ↔ Resistivity

σ = 1 / ρ

Quick answer

This calculator solves σ = 1 / ρ for Conductivity. With Resistivity 1 µΩ·m, the result is 1 MS/m. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Conductivity (S/m)
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Formula

σ = 1 / ρ

Description

Conductivity and resistivity are reciprocal material properties: conductivity measures how easily a material carries current, resistivity how strongly it opposes it. They are intrinsic to the material and independent of its shape, unlike resistance. Conductivity is convenient for good conductors, resistivity for insulators and for computing resistance from geometry (R = ρ·L/A).

Variables

  • σ — Conductivity (S/m)
  • ρ — Resistivity (Ω·m)

Practical Notes

Copper: ρ ≈ 1.72×10⁻⁸ Ω·m, σ ≈ 5.8×10⁷ S/m. Both vary with temperature; conductivity falls as a metal heats up. Resistance follows from R = ρ·L/A = L/(σ·A).

Symbols and units

Symbol Meaning Default unit Accepted units
sigma Conductivity S/m S/m, kS/m, MS/m
rho Resistivity Ω·m nΩ·m, µΩ·m, mΩ·m, Ω·m

Step by step

  1. 1. What you know: Resistivity 1 µΩ·m
  2. 2. The relation: σ = 1 / ρ
  3. 3. Substitute: rho = 1 µΩ·m
  4. 4. Result: Conductivity = 1 MS/m

Worked examples

Minimum range

Given: Resistivity 1 nΩ·m

Result: Conductivity = 1000 MS/m

Low range

Given: Resistivity 10 nΩ·m

Result: Conductivity = 100 MS/m

Typical

Given: Resistivity 1 µΩ·m

Result: Conductivity = 1 MS/m

High range

Given: Resistivity 1 mΩ·m

Result: Conductivity = 1 kS/m

Maximum range

Given: Resistivity 10 mΩ·m

Result: Conductivity = 100 S/m

Solving for each variable

Solve for Conductivity

Resistivity 1 nΩ·m → 1000 MS/m

Solve for Resistivity

Conductivity 1 kS/m → 1 mΩ·m

How Conductivity changes with Resistivity

Resistivity (input) Conductivity (result)
100 nΩ·m 10 MS/m
0.25 µΩ·m 4 MS/m
0.5 µΩ·m 2 MS/m
0.75 µΩ·m 1.333 MS/m
1 µΩ·m 1 MS/m
1.5 µΩ·m 0.6667 MS/m
2 µΩ·m 0.5 MS/m
4 µΩ·m 0.25 MS/m
7 µΩ·m 142.9 kS/m
10 µΩ·m 100 kS/m

The same result in other units

Unit Value
S/m 1000000
kS/m 1000
MS/m 1

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Frequently asked questions

How do you calculate Conductivity ↔ Resistivity?

Use σ = 1 / ρ. With Resistivity 1 µΩ·m, Conductivity works out to 1 MS/m.

What is the formula for Conductivity ↔ Resistivity?

The formula is σ = 1 / ρ. Conductivity and resistivity are reciprocal material properties: conductivity measures how easily a material carries current, resistivity how strongly it opposes it.

How do you find Resistivity when you know the other values?

Rearrange for Resistivity: with Conductivity 1 kS/m, Resistivity is 1 mΩ·m.

What units does Conductivity ↔ Resistivity use?

Conductivity is shown in S/m, kS/m, MS/m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Fields & Electromagnetism formulas →
Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Conductivity ↔ Resistivity

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