Resistivity Calculator converts resistance, length, and area into resistivity, conductivity, percent IACS, conductance, equivalent wire diameter, and power loss, calculated instantly.
Turning a Measured Resistance Into a Material Property
Pouillet’s Law defines resistivity as $$\rho = \frac{R \cdot A}{L}$$, where R is the sample’s measured resistance in ohms, A is its cross-sectional area, and L is the length of the current path, both converted to meters and square meters.
The relationship comes from rearranging $R = \rho L / A$ — the version of the formula that describes how resistance grows with length and shrinks with area — to isolate the one quantity that stays constant no matter how the sample is cut: ρ.
Entering resistance in kilohms or megohms, length in inches, feet, centimeters, or millimeters, and area in square millimeters, square centimeters, or square inches all get converted to base ohms, meters, and square meters before that division happens.
Conductivity, $$\sigma = \frac{1}{\rho}$$, and conductance, $$G = \frac{1}{R}$$, come directly off the same three inputs — the first describes the material, the second describes only that one sample.
Working Backward From a Nichrome Heating Element
A 1 meter length of nichrome heating wire measures 1.1 ohms end to end, with a cross-sectional area of 1 square millimeter (1 × 10⁻⁶ m²). No unit conversion is needed once those figures are in ohms, meters, and square meters, so the resistivity comes out directly: $$\rho = \frac{1.1 \times 1\times10^{-6}}{1} = 1.10\times10^{-6}\ \Omega\cdot m$$, which sits at the low end of nichrome’s published range of 1.10–1.50 × 10⁻⁶ Ω·m.
Conductivity follows as σ ≈ 909,091 S/m, or about 1.57% IACS — a small fraction of copper’s conductivity, which is expected from an alloy chosen for resisting current rather than carrying it efficiently.
Conductance for this specific 1 meter sample is G ≈ 0.909 siemens, and treating the area as if it belonged to a round conductor gives an equivalent diameter of about 1.13 mm, or roughly 1,974 circular mils on an American wire gauge table.
Per meter of length, the wire drops 1.1 volts for every amp pushed through it, and running exactly 1 amp through it dissipates 1.1 watts at a current density of 1 A/mm².
Where the Result Lands Against Copper, Aluminum, and Nichrome
A resistivity of 1.72 × 10⁻⁸ Ω·m belongs to annealed copper — the reference point behind the %IACS figure, fixed at a conductivity of 58,000,000 S/m no matter what material is actually being tested. Silver comes in slightly lower, around 1.59 × 10⁻⁸ Ω·m, making it more conductive than the copper standard itself. Aluminum sits close to 2.82 × 10⁻⁸ Ω·m, and resistive alloys like nichrome run four orders of magnitude higher.
| Material | Typical resistivity (Ω·m) | Approx. %IACS |
|---|---|---|
| Silver | 1.59 × 10⁻⁸ | ~106% |
| Copper (annealed) | 1.72 × 10⁻⁸ | 100% (reference) |
| Aluminum | 2.82 × 10⁻⁸ | ~61% |
| Nichrome | 1.10–1.50 × 10⁻⁶ | ~1.1–1.6% |
A low %IACS reading isn’t a defect — it only means the sample conducts poorly relative to copper on a scale where copper is fixed at 100 by definition. Insulators, resistor windings, and heating elements are all working correctly with a %IACS in the low single digits or less.
Why a Diameter Measurement Error Hurts More Than a Length Error
Area, not length, absorbs the most error. Resistivity scales linearly with the area entered, but if that area was derived outside the calculator from a diameter reading, $A = \pi(d/2)^2$ means a 2% error in the diameter becomes roughly a 4% error in the area — and an equal 4% error in the resulting resistivity.
A length error of the same size propagates one-to-one instead of doubling. Resistance and geometry also sit on different sides of a validation boundary: R = 0 is accepted and reported as an infinite-conductivity superconductor, while length and area must be strictly greater than zero or the calculation halts.
Every figure tied to a current load — power loss, per-meter loss, current density — is computed at a fixed 1 amp reference rather than the sample’s actual operating current; because power scales with current squared, doubling the real current quadruples those figures rather than doubling them.
Common Questions About Converting Resistance to Resistivity
What’s the difference between resistance and resistivity?
Resistance is a property of one specific object and depends on that object’s length and cross-sectional area as well as its material. Resistivity is intrinsic to the material alone: two nichrome wires of different lengths and thicknesses have different resistances but the same resistivity, provided the alloy and temperature match.
Can resistivity be zero or negative?
Input validation only requires R to be at least zero — length and area must be strictly positive or the calculation won’t run at all. A measured resistance of exactly 0 ohms returns an infinite-conductivity result, the mathematical stand-in for a superconducting or zero-resistance connection.
What does %IACS actually measure?
%IACS measures conductivity relative to annealed copper, fixed at exactly 58,000,000 S/m regardless of what’s being tested. A reading of 60% IACS means the sample conducts 60% as well as that copper reference — it says nothing about whether that’s good or bad for the intended use.
Why does the input ask for area instead of diameter?
Area lets the same formula work for round wire, rectangular busbar, or an irregular test coupon without forcing a shape assumption into the input. An equivalent round-wire diameter and circular-mil figure get derived afterward for comparison against wire gauge tables, but the area entered can come from any shape.
What’s a circular mil, and why does it show up here?
A circular mil is the area of a circle exactly one mil (0.001 inch) across, and it’s the standard unit on American wire gauge and busbar sizing tables. Cross-sectional area converts to circular mils at a fixed rate of roughly 1.97 billion cmil per square meter, regardless of the shape the area came from.
Does this account for temperature?
No — the resistance entered is treated as the resistance at whatever temperature it was measured, and the resulting resistivity reflects that same temperature. Resistivity for most metals rises a few tenths of a percent per degree Celsius, so a reading taken hot resolves to a higher resistivity than the same sample measured cold.
What’s the difference between conductance and conductivity?
Conductivity (σ) is the inverse of resistivity and describes the material regardless of shape. Conductance (G) is the inverse of resistance and describes only the one sample measured — a thick, short bar of a poor conductor can have higher conductance than a long, thin wire of a much better one.
What This Result Doesn’t Account For
The resistivity figure reflects the exact resistance, length, and area entered, at whatever temperature that resistance was measured — it carries no built-in temperature correction, no adjustment for AC skin effect at high frequencies, and assumes the material is uniform along the entire measured length.
A sample with a void, a crimp, or a temperature gradient partway through it still produces a single averaged resistivity that may not represent any one point in the material.