Conductivity to Resistivity Calculator

Enter an electrical conductivity value and unit to get the equivalent resistivity (ρ = 1/σ) in Ω·m, Ω·cm, and µΩ·cm, plus an optional conductor resistance estimate.

Quick Facts

Reciprocal relationship
ρ = 1 / σ
Resistivity and conductivity are reciprocals — a highly conductive material always has low resistivity.
Copper reference
σ ≈ 5.96×10⁷ S/m (ρ ≈ 1.68 µΩ·cm)
Annealed copper is the traditional benchmark for the % IACS conductivity scale.
% IACS standard
100% IACS = 5.8001×10⁷ S/m
Used to grade copper and aluminum alloys against annealed copper's conductivity.

Your Results

Calculated
Resistivity
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ρ = 1/σ, in ohm-meters (Ω·m)
Resistivity
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Same value in ohm-centimeters (Ω·cm)
Resistivity
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Same value in microhm-centimeters (µΩ·cm)
Estimated Conductor Resistance
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R = ρL/A for the entered length and cross-section

Ready

Enter a conductivity value and unit, then press Calculate.

Formula and Method for Converting Conductivity to Resistivity

Electrical conductivity (σ, sigma) measures how easily a material carries electric current, expressed in siemens per meter (S/m). Electrical resistivity (ρ, rho) measures how strongly that same material opposes current flow, expressed in ohm-meters (Ω·m). The two quantities are reciprocals of one another: ρ = 1 / σ. A material that conducts well — like copper — has a very small resistivity, while a poor conductor has a large one. This calculator converts a conductivity value in any common unit into resistivity in Ω·m, Ω·cm, and µΩ·cm, and can also estimate the resistance of a specific conductor from its length and cross-sectional area.

How the calculation works

Enter the conductivity value and choose its unit. The calculator first converts that value to the SI base unit, siemens per meter, using standard factors (1 kS/m = 1,000 S/m; 1 MS/m = 1,000,000 S/m; 1 S/cm = 100 S/m; and 1% IACS = 5.8001×10⁵ S/m, since 100% IACS is defined as 5.8001×10⁷ S/m). It then takes the reciprocal to get resistivity in Ω·m (ρ = 1/σ), and converts that into Ω·cm (× 100) and µΩ·cm (× 10⁸), the units most often quoted for metals. If you supply a conductor length (in meters) and cross-sectional area (in mm²), the tool also applies R = ρL/A — converting the area to m² first — to estimate the conductor's total resistance.

Common mistakes

  • Confusing conductivity and resistivity: they move in opposite directions — a bigger conductivity number means a smaller resistivity, not a bigger one.
  • Mixing up unit prefixes: S/m, kS/m, and MS/m differ by factors of 1,000, and S/cm is 100 times larger than S/m — always double-check which unit a data sheet is using.
  • Treating % IACS as an absolute unit: it is a percentage relative to annealed copper (100% IACS = 5.8001×10⁷ S/m), not a conductivity value you can plug directly into ρ = 1/σ without converting first.
  • Mismatched area units in R = ρL/A: resistivity is in Ω·m, so the area must be in m² (not mm² or cm²) before dividing, or the resistance will be off by several orders of magnitude.

Real-world applications

  • Wire and cable sizing: comparing the resistivity of copper versus aluminum conductors to balance weight, cost, and voltage drop over a given run length.
  • Quality control: testing formed or heat-treated metal parts against a target % IACS to confirm the alloy and temper meet specification.
  • Grounding and busbar design: using resistivity and cross-section to estimate the resistance and I²R heating of a conductor before it is installed.
  • Materials science: characterizing thin films, doped semiconductors, and new alloys by converting measured conductivity into resistivity for comparison with reference tables.

Frequently Asked Questions

What is the difference between conductivity and resistivity?
Electrical conductivity (σ) measures how easily a material carries electric current, in siemens per meter (S/m). Resistivity (ρ) measures how strongly a material opposes that current, in ohm-meters (Ω·m). They are reciprocals of each other: ρ = 1/σ, so a material with high conductivity always has low resistivity.
How do I convert conductivity in MS/m to resistivity in µΩ·cm?
First convert the conductivity to S/m by multiplying by 10⁶ (1 MS/m = 1,000,000 S/m). Take the reciprocal to get resistivity in Ω·m, multiply by 100 to get Ω·cm, then by 1,000,000 to get µΩ·cm. For example, 58 MS/m converts to about 1.72×10⁻⁸ Ω·m, or 1.72 µΩ·cm.
What does % IACS mean?
% IACS (International Annealed Copper Standard) expresses a metal's conductivity relative to annealed copper, where 100% IACS is defined as 5.8001×10⁷ S/m. It is widely used to grade copper and aluminum alloys and to check heat-treatment quality — most wrought aluminum alloys fall roughly between 30% and 62% IACS.
How do I estimate a wire's resistance from its resistivity?
Use R = ρ × L / A, where ρ is the resistivity in ohm-meters, L is the conductor length in meters, and A is the cross-sectional area in square meters. For example, 100 m of copper wire (ρ ≈ 1.68×10⁻⁸ Ω·m) with a 1.5 mm² cross-section has a resistance of about 1.12 Ω.

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