How this instrument works
Conductivity and resistivity describe the same physical fact from opposite sides. Conductivity, σ, measured in siemens per metre, says how much current density a material carries for a given electric field — a high σ means charge moves freely. Resistivity, ρ, in ohm-metres, says how strongly that same material opposes the flow. Ohm's law in its local form, J = σE, rearranges to E = ρJ, and comparing the two forces ρ = 1 ⁄ σ directly out of the algebra, not from any measured curve fit.
The formula carries no fitted constant and no conversion factor, because the siemens and the ohm are themselves reciprocal units by SI definition — one siemens equals one ohm to the power minus one. That is why this instrument needs only a single division: enter σ and 1 ⁄ σ is the entire calculation, no lookup table or correction term required. Contrast that with resistance, which additionally depends on a conductor's length and cross-sectional area rather than on the material alone.
The clean reciprocal assumes an isotropic, ohmic conductor held at one fixed temperature. In a single crystal, a magnetized plasma, or certain layered composites, conductivity is direction-dependent — a tensor rather than one number — so a scalar σ measured along one axis will not correctly predict ρ along another. And because resistivity climbs with temperature in metals, copper's rising roughly 0.393 percent per degree Celsius near 20°C, a conductivity figure is only ever paired correctly with the resistivity taken at that same temperature.
- Enter the material's conductivity into the Electrical conductivity, S⁄m field — pull the figure from a materials table or your own four-point-probe reading.
- No unit menu to set: σ is read in siemens per metre and ρ comes out in ohm-metres, matching the SI definition, so there is nothing to convert first.
- The instrument inverts the value instantly using ρ = 1 ⁄ σ — no intermediate steps.
- Read the answer in the Resistivity, Ω·m field, reported to ten significant figures for downstream calculations like R = ρL⁄A.
- To go the other way, invert a known resistivity yourself (σ = 1 ⁄ ρ) before typing it in, since this instrument's single input field is conductivity.
Worked example — copper's conductivity inverted to resistivity
Copper's standard conductivity figure, quoted in materials tables as σ = 5.96 × 10⁷ S⁄m (that is, 59,600,000 S⁄m), goes straight into the sigma field. The instrument returns ρ = 1 ⁄ 59,600,000 = 1.67785234899 × 10⁻⁸ Ω·m — the textbook copper resistivity of about 1.68 × 10⁻⁸ Ω·m at 20°C, recovered to ten decimal places because the relationship is a definition rather than a fitted approximation.
That resistivity is the starting point a cable engineer reaches for when sizing a conductor: resistance follows from R = ρL⁄A, so a 10-metre run of 25 mm² copper busbar works out to R = (1.67785 × 10⁻⁸ × 10) ⁄ (25 × 10⁻⁶) ≈ 0.00671 Ω. That is trivial for a lighting circuit but matters on a long low-voltage DC run at high current, where every extra milliohm shows up as heat and lost volts at the far end.
Questions
Why are conductivity and resistivity exact reciprocals rather than just related quantities?
Because that is how each is defined. Ohm's law in local form reads J = σE, or equivalently E = ρJ; substituting one expression into the other forces ρ = 1 ⁄ σ by algebra alone, not by any empirical curve-fit. The product ρσ therefore equals exactly 1 for an isotropic ohmic material, at whatever temperature the two figures were measured.
Does this reciprocal formula still work for semiconductors and insulators?
Yes, provided the material is ohmic at the point you are measuring — its current stays proportional to the applied field there. Diodes, transistors in saturation, and other nonlinear devices do not have one fixed σ, so a resistivity computed from a single operating point will not hold at another; the reciprocal is still true instantaneously, just not usefully constant across the device's range.
Why does this example use 5.96 × 10⁷ S⁄m instead of the IACS reference value of 5.80 × 10⁷ S⁄m?
Both are real numbers for real copper. The 1913 International Annealed Copper Standard fixes 100% conductivity at 5.80 × 10⁷ S⁄m (1.7241 × 10⁻⁸ Ω·m); well-annealed high-purity copper of the kind quoted in modern materials tables measures closer to 5.96 × 10⁷ S⁄m, about 103% IACS. Good commercial copper simply outperforms the century-old reference sample, and this is the higher, commonly tabulated figure.
How is resistivity different from resistance?
Resistivity, in ohm-metres, is a bulk material property independent of shape; resistance, in ohms, is what a specific object made from that material presents to current, found from R = ρL⁄A using its length L and cross-sectional area A. Doubling a wire's length doubles its resistance without changing its resistivity at all — this instrument produces the material property, not the resistance of any one wire.
Does temperature change the answer?
Yes — both σ and ρ are temperature-dependent, so the reciprocal only holds at the temperature the conductivity figure was measured at. Copper's resistivity rises about 0.393 percent per degree Celsius near room temperature, so a σ value taken at 20°C will not give the correct ρ at 100°C; look up or measure conductivity at the temperature that actually matters for your circuit.
What happens if I enter a conductivity of zero?
The instrument rejects it, because 1 ⁄ σ is undefined at zero and every real conductor has σ greater than zero. A material with very low conductivity, such as a ceramic insulator, simply pushes the resulting resistivity toward a very large but still finite number rather than to infinity in practice.