The conductivity to resistivity calculator above handles a conversion that looks trivial and is not. The two quantities are exact reciprocals, so one division does the arithmetic — but the numbers that come out are only meaningful at a stated temperature, and turning them into the resistance of a real conductor needs geometry as well. This page does all three steps and shows each one, so you can see whether the answer you needed was the material property or the object's resistance.
Arb Digital builds free calculators that make the difference between a material property and an object property explicit, because conflating the two is the single most common error in this area. Resistivity belongs to the substance. Resistance belongs to a specific length and thickness of it. Once a length and a diameter are entered here, the tool reports both, and the Ohm's law calculator takes that resistance on to voltage and current.
What This Conductivity to Resistivity Calculator Does
Enter either quantity and it returns the other, since conductivity is one divided by resistivity and the relationship holds exactly in both directions. Choose a material from the list and it fills in a reference resistivity at 20 °C together with the temperature coefficient for that substance, so you do not have to look either up.
It then corrects the value to your operating temperature using the standard linear approximation, and reports the percentage change from the reference value. That correction matters far more than people expect: a copper conductor running at 90 °C has about 27 per cent more resistance than the same conductor at 20 °C, which shows up directly as extra voltage drop and extra heating.
Finally it computes the resistance of a conductor of the length and diameter you specify, along with its cross-sectional area. This is the number most practical questions are really after, and it is where the geometry enters: resistance rises in proportion to length and falls in proportion to area, which means with the square of the diameter.
How to Use It
- Pick a material or leave it on custom. Choosing one populates the reference resistivity and temperature coefficient; custom leaves both fields under your control.
- Choose which quantity you are starting from. Resistivity in ohm-metres or conductivity in siemens per metre — the other is derived immediately.
- Set the operating temperature. The reference values are quoted at 20 °C, and the correction is applied from there.
- Enter the conductor length and diameter. These give the cross-sectional area and, with the corrected resistivity, the resistance.
- Read the percentage change. It tells you at a glance whether the temperature correction is negligible for your purposes or the dominant effect.
The Formula: How the Conversion Works
Conductivity σ is defined as the reciprocal of resistivity ρ, so σ = 1/ρ and ρ = 1/σ. Resistivity is measured in ohm-metres and conductivity in siemens per metre, the siemens being the reciprocal ohm and a coherent derived unit of the SI, as listed in the SI Brochure published by the BIPM. There is no scaling factor hidden in the conversion; the units are constructed to make it a plain reciprocal.
The resistance of a uniform conductor follows from R = ρL/A, where L is its length along the current path and A is the cross-sectional area perpendicular to it. OpenStax University Physics Volume 2, section 9.3 on resistivity and resistance, gives this relation together with Table 9.1, "Resistivities and Conductivities of Various Materials at 20 °C", which is the source of the material values and temperature coefficients offered in the dropdown above.
Temperature is handled with the linear approximation ρ ≈ ρ0[1 + α(T − T0)], also stated on that page, where α is the temperature coefficient of resistivity and T0 is the reference temperature. Work the defaults: copper at 20 °C has ρ = 1.68 × 10−8 Ω·m, so σ = 5.952 × 107 S/m. A 2 mm diameter gives A = π × 0.0012 = 3.1416 × 10−6 m2, and ten metres of it has R = 1.68 × 10−8 × 10 ÷ 3.1416 × 10−6 = 0.0535 Ω.
Why Temperature Correction Is Not Optional
Take that same copper conductor to 90 °C. The correction factor is 1 + 0.0039 × 70 = 1.273, so the resistivity becomes 2.139 × 10−8 Ω·m and the ten-metre resistance rises to 0.0681 Ω. That is 27.3 per cent more resistance, 27.3 per cent more voltage drop at the same current, and 27.3 per cent more heat dissipated in the conductor.
The feedback is what makes it interesting. More resistance produces more heating, which raises the temperature further, which raises the resistance again. In a well-designed installation the process settles at a stable operating point. In a poorly ventilated one, or where a connection has degraded and is generating heat locally, it can run away — which is the physical mechanism behind failures at loose terminals.
Cable rating tables account for this by specifying conductor temperature limits and derating factors for grouping and ambient conditions. If you are sizing a real run rather than exploring the physics, the wire size calculator and the voltage drop calculator work in those practical terms, and both depend on exactly the relationship shown here.
Positive and Negative Coefficients
Metals get worse at conducting as they warm. Their conduction electrons are scattered by thermal vibration of the lattice, and hotter lattices vibrate more, so the coefficient is positive — typically around 0.004 per degree for common metals, which is why a fivefold difference between them is unusual while a thirty per cent temperature effect is routine.
Carbon and semiconductors behave in the opposite way. Warming them liberates more charge carriers than it costs in extra scattering, so resistivity falls and the coefficient is negative. This is why a carbon composition resistor drifts downward with temperature, why a thermistor can be made deliberately sensitive in either direction, and why silicon is a poor conductor at room temperature but an increasingly good one when heated.
Nichrome sits in a useful middle ground. Its resistivity is nearly sixty times that of copper and its coefficient is roughly a tenth of copper's, which is exactly what a heating element needs: enough resistance to dissipate real power in a manageable length of wire, and enough stability that the power does not swing wildly as the element comes up to temperature.
Resistivity, Resistance and the Geometry Between Them
The relation R = ρL/A carries a trap in the area term. Doubling the length doubles the resistance, which is intuitive. Doubling the diameter quarters it, because area goes with the square of diameter — and that is why a modest increase in conductor size is such an effective fix for a voltage-drop problem, and why crimping or corroding a connection down to a fraction of its cross-section raises local resistance so sharply.
It also explains why cable sizes progress in the steps they do. Each standard size up increases the area by a roughly constant ratio, so each step buys a roughly constant percentage reduction in resistance. If you need the area from a diameter or a set of dimensions, the cross-sectional area calculator handles the geometry, and the resistance converter rescales the result between ohms, milliohms and kilohms.
Where This Simple Model Stops Being Accurate
Three limits are worth knowing. First, the linear temperature correction is an approximation valid over a moderate range around the reference point; across hundreds of degrees the true behaviour curves and a single coefficient overstates or understates the change. Second, at alternating-current frequencies the skin effect pushes current toward the outside of the conductor, so the effective area is smaller than the physical area and the resistance is higher than this calculation gives — negligible at fifty or sixty hertz for small conductors, significant for large ones and at radio frequencies.
Third, the model assumes a uniform, isotropic material with a constant cross-section. Stranded cable, plated surfaces, work-hardened bends and alloys whose composition varies all depart from that. For most engineering estimates the departures are small; for precision measurement they are not, which is why standards bodies specify measurement conditions in detail rather than relying on a table value.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Confusing resistivity with resistance — the first is a property of the material in ohm-metres, the second a property of a particular object in ohms.
- Ignoring the operating temperature — a copper conductor at 90 °C has around 27 per cent more resistance than the same conductor at 20 °C.
- Using diameter where area is required — resistance falls with the square of diameter, so treating the two as interchangeable is a large error.
- Mixing millimetres and metres — the diameter field expects millimetres while resistivity is in ohm-metres, and the tool converts between them for you.
- Applying the linear coefficient far from its reference — it is an approximation around 20 °C, not a description of behaviour across hundreds of degrees.
Related Free Tools From Arb Digital
Take the resistance figure onward with the Ohm's law calculator, or into a network with the resistor combination calculator and the current divider calculator. For practical cable work use the wire size calculator and the voltage drop calculator. Geometry comes from the cross-sectional area calculator, unit rescaling from the resistance converter, and temperature conversion from the temperature converter. The full free online tools hub lists everything else.
Frequently Asked Questions
They are exact reciprocals. Conductivity in siemens per metre is one divided by resistivity in ohm-metres, and the units are constructed so that no scaling factor is involved in the conversion.
Resistivity is a property of the material alone, quoted in ohm-metres. Resistance is a property of a specific object and depends on its length and cross-sectional area as well as on what it is made of.
In metals, thermal vibration of the lattice scatters conduction electrons more at higher temperature, so resistivity rises. In carbon and semiconductors, warming frees more charge carriers than it costs in scattering, so resistivity falls instead.
With a coefficient of about 0.0039 per degree, the correction factor across seventy degrees is roughly 1.27, so both the resistivity and the resistance of a copper conductor rise by about twenty-seven per cent.
Because resistance depends on cross-sectional area, and area grows with the square of the diameter. Twice the diameter is four times the area, so a quarter of the resistance for the same length and material.
Only approximately. At higher frequencies the skin effect concentrates current near the surface, reducing the effective area and raising resistance above the direct-current value this calculation gives.
Because its resistivity is far higher than copper's, so a manageable length dissipates useful power, and its temperature coefficient is small, so the power does not swing much as the element heats up.
This tool is provided for educational and estimating use. It applies an idealised uniform-conductor model with a linear temperature correction, and does not account for skin effect, stranding, plating, installation conditions or wiring regulations.
