Conductivity to Resistivity Calculator
Convert electrical conductivity (σ) to resistivity (ρ) instantly using ρ = 1/σ. Free online physics calculator with material presets for silver, copper, gold, aluminum, and more.
About This Calculator
The Conductivity to Resistivity Calculator converts between electrical conductivity (σ) and electrical resistivity (ρ) using the fundamental relationship ρ = 1/σ. Electrical conductivity measures a material's ability to conduct electric current, while electrical resistivity measures how strongly it opposes current flow. These are intrinsic material properties that do not depend on the dimensions of the material but rather on its composition, charge carrier density, and temperature.
The calculator includes built-in material presets for common conductors including silver (6.29 × 10⁷ S/m), copper (5.96 × 10⁷ S/m), gold (4.10 × 10⁷ S/m), aluminum (3.77 × 10⁷ S/m), tungsten (1.79 × 10⁷ S/m), iron (1.03 × 10⁷ S/m), platinum (9.43 × 10⁶ S/m), nichrome (9.09 × 10⁵ S/m), and carbon (2.86 × 10⁴ S/m). Selecting a material automatically populates its conductivity value, or you can enter a custom value manually.
Formula
The conversion formula is: ρ = 1 / σ, where ρ is resistivity in ohm-meters (Ω·m) and σ is conductivity in siemens per meter (S/m). Since conductivity and resistivity are reciprocals, a material with high conductivity (like silver) has very low resistivity, while an insulator with low conductivity has extremely high resistivity.
Classification
Based on the calculated resistivity, the calculator classifies materials into three categories: Conductors (resistivity below 10⁻⁴ Ω·m, including metals like copper and silver), Semiconductors (resistivity between 10⁻⁴ and 10⁷ Ω·m, including silicon and carbon), and Insulators (resistivity above 10⁷ Ω·m, including glass, rubber, and plastic).
Applications
This calculator is useful for electrical engineers selecting wire materials, physics students studying electrical properties of matter, electronics hobbyists designing circuits, and materials scientists comparing conductive properties. Understanding the conductivity-to-resistivity relationship is fundamental to Ohm's law, circuit design, power transmission, and semiconductor physics.
Frequently Asked Questions
How do I convert conductivity to resistivity?
Electrical resistivity ρ is the reciprocal of electrical conductivity σ. Use the formula ρ = 1/σ. For example, if conductivity is 5.96 × 10⁷ S/m (copper), resistivity = 1 / (5.96 × 10⁷) = 1.68 × 10⁻⁸ Ω·m.
What is the difference between conductivity and resistivity?
Conductivity (σ) measures how easily a material allows electric current to flow, while resistivity (ρ) measures how strongly a material opposes current flow. They are reciprocal properties: high conductivity means low resistivity and vice versa. Conductors like silver and copper have high conductivity, while insulators like glass and Teflon have very low conductivity.
What are the SI units for conductivity and resistivity?
The SI unit of electrical resistivity is the ohm-meter (Ω·m). The SI unit of electrical conductivity is siemens per meter (S/m), which is equivalent to (Ω·m)⁻¹.
What is the conductivity of silver?
Silver has the highest electrical conductivity of any metal at approximately 6.29 × 10⁷ S/m at 20°C, corresponding to a resistivity of 1.59 × 10⁻⁸ Ω·m. This makes silver the best conductor, though copper (5.96 × 10⁷ S/m) is more commonly used in electrical wiring due to lower cost.
How does temperature affect conductivity and resistivity?
For most conductors, resistivity increases with temperature (positive temperature coefficient) while conductivity decreases. This is because higher temperatures cause increased lattice vibrations in the material, which scatter electrons and impede current flow. The relationship is approximately linear: ρ(T) = ρ₀[1 + α(T − T₀)], where α is the temperature coefficient.
What materials are classified as conductors, semiconductors, and insulators?
Conductors (resistivity < 10⁻⁴ Ω·m) include silver, copper, gold, and aluminum. Semiconductors (resistivity 10⁻⁴ to 10⁷ Ω·m) include silicon and germanium whose conductivity can be modified by doping. Insulators (resistivity > 10⁷ Ω·m) include glass, rubber, Teflon, and plastic which strongly resist current flow.
Can I calculate resistivity from conductivity for any material?
Yes, the formula ρ = 1/σ applies universally to all materials. Select a material from the dropdown (silver, copper, gold, aluminum, tungsten, iron, platinum, nichrome, carbon) or enter a custom conductivity value. The calculator will instantly compute the corresponding resistivity and classify the material as a conductor, semiconductor, or insulator.