Convert between electrical conductivity (σ) and resistivity (ρ). Material database, temperature correction, %IACS, and wire resistance.
Electrical conductivity (σ) and resistivity (ρ) are reciprocals: ρ = 1/σ. Conductivity measures how easily a material conducts current (in Siemens per meter, S/m), while resistivity measures how strongly it resists current flow (in ohm-meters, Ω·m). Both are intrinsic material properties that depend on temperature.
The relationship is simple — ρ = 1/σ — but converting between the many unit systems (µΩ·cm, Ω·mm²/m, %IACS, MS/m, nΩ·m) requires careful attention. Temperature also has a significant effect: copper resistivity increases about 0.4% per °C, so a wire at 75°C has 22% more resistance than at 20°C.
This calculator converts between conductivity and resistivity in any common unit, includes a database of 15 common materials, applies temperature correction via the linear coefficient α, and calculates wire resistance for practical applications. The IACS (International Annealed Copper Standard) rating shows conductivity as a percentage of annealed copper. Check the example with realistic values before reporting.
Converting between conductivity and resistivity is routine in electrical engineering, materials science, and physics, but the many unit systems (SI, CGS, practical engineering) create confusion. Temperature correction adds another step that is easy to forget but can change resistance by 20%+ in normal operating conditions.
This calculator handles all conversions instantly, supports every common unit system, and provides the temperature-corrected values engineers actually need. The built-in material database serves as a quick reference for common conductors, semiconductors, and insulators.
ρ = 1/σ. Temperature correction: ρ(T₂) = ρ(T₁) × [1 + α(T₂ − T₁)]. Wire resistance: R = ρL/A. IACS: %IACS = (σ / 5.80×10⁷) × 100.
Result: ρ₂₀ = 1.678 µΩ·cm, ρ₇₅ = 2.041 µΩ·cm (100% IACS)
σ = 5.96×10⁷ S/m → ρ = 1.678×10⁻⁸ Ω·m = 1.678 µΩ·cm. At 75°C: ρ = 1.678×10⁻⁸ × (1 + 0.00393 × 55) = 2.041×10⁻⁸ Ω·m. IACS = 5.96×10⁷ / 5.80×10⁷ = 102.8%.
The SI unit of conductivity is the Siemen per meter (S/m). For metals, values are large (copper = 5.96 × 10⁷ S/m), so megasiemens per meter (MS/m) is convenient. The IACS system normalizes to annealed copper: silver is 106% IACS, aluminum is 61% IACS, and brass ranges from 25-37% IACS.
For resistivity, the SI unit is the ohm-meter (Ω·m). Since most metals have resistivities in the 10⁻⁸ Ω·m range, micro-ohm-centimeters (µΩ·cm) is the standard practical unit. The conversion: 1 µΩ·cm = 10⁻⁸ Ω·m = 10⁻⁶ Ω·mm²/m.
Most electrical systems operate above room temperature. A motor winding at 130°C has roughly 43% more resistance than at 20°C and draws proportionally less current — an important factor in motor starting calculations. Power transformers are rated for maximum temperature rise (65°C or 80°C above ambient) partly because winding resistance increases with temperature, increasing I²R losses.
In RTD (Resistance Temperature Detector) sensors, this temperature dependence is exploited for precise temperature measurement. Platinum (α = 0.003927/°C) is the standard because its relationship is highly linear and repeatable.
For a wire of length L (meters) and cross-section A (mm²): R = ρ × L / A, where ρ is in Ω·mm²/m. For copper at 20°C, ρ = 0.01724 Ω·mm²/m. A 100-meter run of 2.5 mm² copper wire has R = 0.01724 × 100 / 2.5 = 0.69 Ω. At 10A, this drops 6.9V and dissipates 69W — significant in long runs.
100% IACS (International Annealed Copper Standard) = 5.80 × 10⁷ S/m at 20°C. Modern annealed copper actually exceeds this at ~103% IACS. Silver is ~106% IACS. Aluminum is ~61% IACS.
Higher temperature increases lattice vibrations (phonons), which scatter conduction electrons more frequently. This increases resistance. The linear approximation ρ(T) = ρ₀[1 + α(T − T₀)] works well for metals over moderate temperature ranges.
In semiconductors, higher temperature creates more charge carriers (electrons jump from valence to conduction band). This increased carrier concentration outweighs the increased scattering, so resistivity decreases with temperature.
Ω·m (SI), µΩ·cm (most common for metals — copper is 1.68 µΩ·cm), Ω·mm²/m (convenient for wire calculations — numerically same as µΩ·cm × 100), and nΩ·m (=0.1 µΩ·cm).
Nichrome has high resistivity (~110 µΩ·cm vs 1.7 for copper), a very low temperature coefficient (α = 0.0004/°C vs 0.004 for copper), and excellent oxidation resistance at high temperatures. The stable resistance means consistent heating power.
For metals, ρ(T) = ρ₀[1 + α(T − T₀)] is accurate to within 1-2% over ranges of ±100°C from the reference. For wider ranges, a quadratic correction or Bloch-Grüneisen model is needed.