Conductivity to Resistivity Calculator – Convert σ to ρ
Convert electrical conductivity (S/m) to resistivity (Ω·m) instantly using the fundamental relationship ρ = 1/σ for any material.
Enter the electrical conductivity in Siemens per metre (S/m). Optionally enter the temperature (°C) and material name for reference. The calculator returns the resistivity in Ohm-metres (Ω·m).
Conductivity to Resistivity Calculator – Convert σ to ρ
Convert electrical conductivity (S/m) to resistivity (Ω·m) instantly using the fundamental relationship ρ = 1/σ for any material.
About the Conductivity to Resistivity Calculator
Electrical conductivity (σ) and resistivity (ρ) are two complementary ways to express how well a material conducts electric current. They are inversely related by the fundamental equation ρ = 1/σ (or equivalently σ = 1/ρ). Conductivity is measured in Siemens per metre (S/m) and describes how easily current flows through a material, while resistivity is measured in Ohm-metres (Ω·m) and describes how strongly a material opposes current flow. A high-conductivity material has low resistivity, and vice versa.
The range of conductivity values across materials spans more than 25 orders of magnitude — one of the widest ranges of any physical property. Excellent conductors like silver (σ ≈ 6.3 × 10⁷ S/m) and copper (σ ≈ 5.8 × 10⁷ S/m) sit at one extreme, with resistivities around 1–2 × 10⁻⁸ Ω·m. Semiconductors such as silicon (σ ≈ 4.4 × 10⁻⁴ S/m intrinsic) occupy a wide middle range, and insulators like glass (σ ≈ 10⁻¹² S/m) and rubber (σ ≈ 10⁻¹⁴ S/m) sit at the opposite extreme with resistivities in the teraohm-metre range.
Both properties depend on temperature. For metals, resistivity increases with temperature because increased thermal vibration of lattice atoms scatters conduction electrons more strongly. This relationship is approximately linear: ρ(T) = ρ₀[1 + α(T − T₀)], where α is the temperature coefficient of resistivity, typically around 0.003–0.006 per °C for common metals. For semiconductors, the relationship is reversed — resistivity decreases with increasing temperature because thermal energy promotes more electrons into the conduction band.
In electrical engineering, resistivity is used to calculate the resistance of a wire or conductor: R = ρL/A, where L is the length and A is the cross-sectional area. Choosing the right material for a given application requires balancing resistivity (for conductors: lower is better to reduce energy loss), cost, weight, mechanical properties, and thermal behavior. Copper dominates power distribution due to its combination of very low resistivity, adequate mechanical strength, and reasonable cost. Aluminum, with slightly higher resistivity (ρ ≈ 2.8 × 10⁻⁸ Ω·m), is preferred for overhead transmission lines due to its much lower density.
In semiconductor device physics, precise control of conductivity through doping is the foundation of transistors, diodes, and integrated circuits. Adding small concentrations of dopant atoms (boron or phosphorus for silicon) can increase conductivity by many orders of magnitude, enabling the creation of p-type and n-type regions essential for electronic devices. Measuring resistivity using four-point probe techniques is a standard quality control step in semiconductor wafer manufacturing.
Conductivity to Resistivity Examples
Common materials and their electrical conductivity and resistivity values at room temperature.
| Material & Conductivity | Resistivity | Application |
|---|---|---|
| Copper: σ = 5.8 × 10⁷ S/m | ρ ≈ 1.72 × 10⁻⁸ Ω·m | Standard electrical wiring; excellent conductor with low cost and good ductility. |
| Aluminum: σ = 3.5 × 10⁷ S/m | ρ ≈ 2.86 × 10⁻⁸ Ω·m | Overhead power lines; higher resistivity than copper but much lighter — preferred for long-distance transmission. |
| Silicon (intrinsic): σ = 4.35 × 10⁻⁴ S/m | ρ ≈ 2300 Ω·m | Undoped silicon is a semiconductor; resistivity drops dramatically when doped with boron or phosphorus. |
| Silver: σ = 6.3 × 10⁷ S/m | ρ ≈ 1.59 × 10⁻⁸ Ω·m | Best electrical conductor among common metals; used in high-performance contacts and solar cells. |
How to Use the Conductivity to Resistivity Calculator
- Enter the electrical conductivity of the material in Siemens per metre (S/m). Use scientific notation for very large or very small values, for example 5.8e7 for copper or 1e-12 for glass.
- Optionally enter the temperature in degrees Celsius for context and documentation. Note that the calculator uses the simple ρ = 1/σ formula — temperature effects are not automatically applied.
- Optionally enter a material name (e.g., Copper, Silicon) for labelling purposes in the result display.
- Click Calculate. The resistivity ρ = 1/σ is computed in Ω·m and the material is classified as conductor, semiconductor, or insulator based on the result.
- Use the example buttons to load common materials: copper, aluminum, or silicon for instant reference values.
Conductivity to Resistivity FAQ
What is the relationship between conductivity and resistivity?
Electrical conductivity (σ) and resistivity (ρ) are exact mathematical inverses: ρ = 1/σ and σ = 1/ρ. Conductivity measures how easily current flows through a material (higher = better conductor), while resistivity measures how strongly a material opposes current flow (lower = better conductor). Both are intrinsic material properties — independent of sample geometry. To find resistance of a specific conductor, use R = ρL/A where L is length and A is cross-sectional area.
What units are used for conductivity and resistivity?
Electrical conductivity is measured in Siemens per metre (S/m), also written as (Ω·m)⁻¹ or mho/m. Resistivity is measured in Ohm-metres (Ω·m). The Siemens (S) is the SI unit of electrical conductance, defined as the reciprocal of the Ohm. Older literature sometimes uses mho (℧) instead of Siemens — they are identical. For thin films and 2D materials, sheet resistance (Ω/square) is used instead of bulk resistivity.
How does temperature affect conductivity and resistivity?
For metals, resistivity increases with temperature: ρ(T) = ρ₀[1 + α(T − T₀)], where α is the temperature coefficient (typically 0.003–0.006 per °C). More lattice vibration at higher temperatures causes more electron scattering and higher resistance. For semiconductors and insulators, resistivity decreases with temperature because thermal energy promotes more charge carriers into the conduction band. Superconductors show zero resistivity below their critical temperature.
What is a typical conductivity value for copper?
Pure annealed copper at 20°C has an electrical conductivity of approximately 5.8 × 10⁷ S/m, corresponding to a resistivity of about 1.72 × 10⁻⁸ Ω·m. This is the IACS (International Annealed Copper Standard) reference value. Cold-working, alloying, or increased temperature all raise the resistivity. Commercially pure copper used in electrical wiring is typically 97–100% IACS. Silver has slightly higher conductivity (~6.3 × 10⁷ S/m) but is much more expensive.
How do I convert conductivity in mS/cm to S/m?
To convert from millisiemens per centimetre (mS/cm) to Siemens per metre (S/m), multiply by 0.1: 1 mS/cm = 0.1 S/m. For example, a water conductivity of 50 mS/cm = 5 S/m. Other conversions: 1 S/cm = 100 S/m; 1 μS/cm = 10⁻⁴ S/m. The calculator requires input in S/m, so always convert to SI units before entering the value.
Can this calculator be used for solutions and electrolytes?
Yes. Electrolytic conductivity (also called specific conductance) is reported in S/m and can be directly entered into this calculator to get the equivalent resistivity. For water and aqueous solutions, conductivity spans from about 5.5 × 10⁻⁶ S/m (ultrapure water) to about 50 S/m (seawater). The ρ = 1/σ relationship is universal and applies to liquids, solids, gases, and plasmas. Note that for electrolytes, conductivity depends strongly on concentration and temperature.