Electrical Conductivity Calculator

Electrical conductivity (σ, sigma) measures how easily electric current flows through a material. It is the inverse of electrical resistivity (ρ, rho). These properties are fundamental to electrical engineering, materials science, and physics.

Key relationships:

Resistivity and Conductivity: σ = 1 / ρ

Where:

• σ = conductivity in siemens per meter (S/m)
• ρ = resistivity in ohm-meters (Ω·m)

Resistance of a wire: R = ρ × L / A

Where:

• R = resistance in ohms (Ω)
• L = length of the conductor (meters)
• A = cross-sectional area (m²)

Conductance: G = 1 / R = σ × A / L

Conductivity values of common materials:

Look at the spread on that table. Copper to rubber is twenty-two orders of magnitude, which is why the chart below uses a log scale and why the same word, “material”, covers both a busbar and the sleeve around it.

Worked example

Ten meters of 2 mm diameter copper wire, at 20°C.

Resistivity = 1 / 5.96×10⁷ = 1.678×10⁻⁸ Ω·m
Cross-section = π × (0.001 m)² = 3.142×10⁻⁶ m²
R = 1.678×10⁻⁸ × 10 / 3.142×10⁻⁶ = 0.0534 Ω, or 53.4 milliohms

Those are the three values the input boxes suggest, so type them in and you get exactly this back. Fifty milliohms sounds like nothing until you push 30 amps through it: that is 48 watts of heat in the wire and a 1.6 volt drop, which on a 12 volt circuit is a lot to lose.

Why copper is used for electrical wiring: Copper has excellent conductivity (second only to silver), is mechanically strong, solderable, and relatively affordable. Silver conducts better but is far more expensive. Aluminum is used in high-voltage transmission lines where weight matters more than resistance: on the table above it carries 63% of copper’s conductivity at less than a third of the density, so per kilogram it wins comfortably.

Temperature effect: Metal conductivity falls as temperature rises, so resistance climbs with heat. The usual linear model is

R(T) = R₂₀ × [1 + α(T - 20)]

where α is the temperature coefficient of resistance, about 0.00393 per °C for copper, 0.00403 for aluminum and 0.0045 for tungsten. Copper wire that measures 1.000 Ω at 20°C measures about 1.118 Ω at 50°C.

Semiconductors do the opposite: heat frees more charge carriers, so conductivity rises with temperature. That sign difference is the whole reason a thermistor works and the reason a silicon device can run away thermally in a way a copper wire never does.