About

Electrical resistivity ρ and conductivity σ are strict reciprocals: ρ = 1 ÷ σ. A factor-of-ten error in unit conversion propagates directly into material selection, wire gauge calculations, and thermal dissipation estimates. Confusing S/m with S/cm introduces a 100× error that can cause conductor overheating or measurement rejection against IEC 60028 and ASTM B193 standards. This calculator performs the reciprocal inversion and handles the metric prefixes so you do not have to track powers of ten manually.

The tool assumes isotropic, homogeneous materials at the measurement temperature you specify. Resistivity is temperature-dependent: copper increases roughly 0.393%/°C above 20°C. Values here correspond to the conductivity you input, not a standardized reference temperature. For anisotropic materials (graphite, single crystals), the scalar relationship breaks down and a tensor treatment is required.

Formulas

The fundamental relationship between conductivity and resistivity is the scalar reciprocal identity, valid for isotropic materials:

ρ = 1σ

Where ρ = electrical resistivity in Ω⋅m, and σ = electrical conductivity in S/m (siemens per metre). The siemens is the reciprocal ohm: 1 S = 1 Ω⁻¹.

Unit prefix conversions applied before inversion:

σ_S/m = σ_input × k_in

Where k_in is the multiplier to convert the chosen input unit to S/m. For example, 1 S/cm = 100 S/m, so k_in = 100. The output resistivity is then scaled by k_out to the desired unit.

ρ_output = 1σ_S/m × k_out

Common output multipliers: 1 Ω⋅m = 100 Ω⋅cm = 10⁶ μΩ⋅m = 10⁸ μΩ⋅cm = 10⁹ nΩ⋅m.

Reference Data

Material	Conductivity σ (S/m)	Resistivity ρ (Ω⋅m)	Temp (°C)	Notes
Silver (Ag)	6.30 × 10⁷	1.59 × 10⁻⁸	20	Highest conductivity of any element
Copper (Cu, annealed)	5.96 × 10⁷	1.68 × 10⁻⁸	20	IACS 100% reference standard
Gold (Au)	4.10 × 10⁷	2.44 × 10⁻⁸	20	Corrosion-resistant contacts
Aluminium (Al)	3.77 × 10⁷	2.65 × 10⁻⁸	20	Overhead power lines
Tungsten (W)	1.79 × 10⁷	5.60 × 10⁻⁸	20	Filament wire
Zinc (Zn)	1.69 × 10⁷	5.90 × 10⁻⁸	20	Galvanization coatings
Nickel (Ni)	1.43 × 10⁷	6.99 × 10⁻⁸	20	Alloy base
Iron (Fe)	1.00 × 10⁷	1.00 × 10⁻⁷	20	Structural, magnetic
Platinum (Pt)	9.43 × 10⁶	1.06 × 10⁻⁷	20	RTD sensors (Pt100)
Tin (Sn)	9.17 × 10⁶	1.09 × 10⁻⁷	20	Solder alloys
Lead (Pb)	4.81 × 10⁶	2.08 × 10⁻⁷	20	Battery plates, shielding
Titanium (Ti)	2.38 × 10⁶	4.20 × 10⁻⁷	20	Aerospace alloys
Stainless Steel 304	1.39 × 10⁶	7.20 × 10⁻⁷	20	Austenitic, non-magnetic
Nichrome (Ni80Cr20)	9.09 × 10⁵	1.10 × 10⁻⁶	20	Heating elements
Graphite (parallel)	3.30 × 10⁵	3.00 × 10⁻⁶	20	Anisotropic; ⊥ is ~10× higher
Carbon (amorphous)	1.25 × 10⁴	8.00 × 10⁻⁵	20	Resistor elements
Seawater	4.80	2.08 × 10⁻¹	25	Electrolyte, ~35 g/L salinity
Drinking Water	5.00 × 10⁻²	2.00 × 10¹	25	Varies by mineral content
Silicon (intrinsic)	1.56 × 10⁻³	6.40 × 10²	20	Undoped semiconductor
Germanium (intrinsic)	2.17	4.60 × 10⁻¹	20	Undoped semiconductor
Deionized Water	5.50 × 10⁻⁶	1.82 × 10⁵	25	18.2 MΩ⋅cm ultra-pure
Glass (soda-lime)	1.00 × 10⁻¹¹	1.00 × 10¹¹	20	Insulator
PTFE (Teflon)	1.00 × 10⁻²⁵	1.00 × 10²⁵	20	Best practical insulator

Frequently Asked Questions

One S/cm equals 100 S/m because there are 100 centimetres in a metre. If you enter a value measured in S/cm but the calculator interprets it as S/m, the computed resistivity will be 100× too high. In wire sizing, that error can lead to selecting a conductor that overheats under load.

The formula ρ = 1 ÷ σ is exact regardless of temperature - the reciprocal relationship is definitional. However, the conductivity value you input is temperature-dependent. For metals, conductivity decreases roughly linearly with temperature. Copper's temperature coefficient is approximately 0.00393 /°C referenced to 20 °C. Always note at which temperature your conductivity was measured.

Yes. The reciprocal relationship holds for any isotropic medium. Intrinsic silicon has a conductivity around 1.56 × 10⁻³ S/m, yielding ρ ≈ 640 Ω⋅m. For electrolytes like seawater (4.8 S/m), the same math applies. Note that doped semiconductors vary by orders of magnitude depending on dopant concentration.

A conductivity of zero implies infinite resistivity - a perfect insulator, which does not physically exist. The calculator rejects zero and negative values and displays an error. If your measurement reads zero, check your instrument calibration or ensure the probe has contact with the sample.

Only partially. Graphite's conductivity parallel to the basal plane is roughly 3.3 × 10⁵ S/m, but perpendicular to it can be 3.3 × 10² S/m - a 1000× difference. For anisotropic materials, conductivity and resistivity become second-rank tensors, and the scalar reciprocal is valid only along a specific crystallographic axis.

The International Annealed Copper Standard defines 100% IACS as 5.80 × 10⁷ S/m (at 20 °C). To convert, multiply the IACS percentage by 5.80 × 10⁵ S/m per percent. For example, aluminium at 61% IACS gives 3.54 × 10⁷ S/m. Enter that value in S/m to get resistivity.