5
×10⁻⁸ Ω·m
2.0000e+15
×10⁶ S/m
0.05
Ω/m
2
S
5
×10⁻⁸ Ω·m
2.0000e+15
×10⁶ S/m
0.05
Ω/m
2
S
The Resistivity and Conductivity Calculator converts between measured resistance values and the intrinsic material properties of resistivity (ρ) and conductivity (σ). While resistance depends on the geometry of a specific sample, resistivity and conductivity are fundamental material constants that characterise how well a substance conducts electricity regardless of its shape or size. These properties are central to material selection in electrical engineering, electronics, and electromagnetic design.
The relationship between resistance, resistivity, and geometry is given by R = ρ × L / A, where R is resistance (Ω), ρ is resistivity (Ω·m), L is the length (m), and A is the cross-sectional area (m²). Rearranging: ρ = R × A / L. Conductivity is simply the reciprocal of resistivity: σ = 1 / ρ, measured in siemens per metre (S/m).
Copper, the benchmark conductor for electrical applications, has a resistivity of approximately 1.72 × 10⁻⁸ Ω·m at 20 °C, corresponding to a conductivity of 5.8 × 10⁷ S/m. The International Annealed Copper Standard (IACS) defines 100% IACS as 5.8 × 10⁷ S/m — all other conductor materials are compared against this reference. Aluminium is about 61% IACS (ρ ≈ 2.82 × 10⁻⁸ Ω·m), making it a less efficient conductor by cross-section but compelling for overhead lines where its lower density (2700 vs 8960 kg/m³) allows lighter, longer spans.
Silver leads all common metals at approximately 6.3 × 10⁷ S/m (108% IACS), but its cost limits its use to specialist applications like RF connectors, high-frequency PCB traces, and satellite components. Gold (45 × 10⁶ S/m) is widely used in connector contacts not for its conductivity but for its corrosion resistance. Tungsten (1.82 × 10⁷ S/m) tolerates extreme temperatures and is used for incandescent lamp filaments and X-ray tube targets.
At the other end of the spectrum, resistance alloys such as Nichrome (ρ ≈ 1.1 × 10⁻⁶ Ω·m) and Kanthal (ρ ≈ 1.4 × 10⁻⁶ Ω·m) are used for heating elements precisely because their high resistivity generates abundant heat. Stainless steel (ρ ≈ 7 × 10⁻⁷ Ω·m) is a poor conductor but mechanically excellent — its presence in cable armouring and structural components is purely for mechanical rather than electrical reasons.
In semiconductor physics, resistivity spans many orders of magnitude: intrinsic silicon has ρ ≈ 640 Ω·m, doped silicon may be as low as 10⁻⁵ Ω·m, and insulators like glass exceed 10¹⁰ Ω·m. The enormous range — more than 20 orders of magnitude from superconductors to insulators — makes resistivity one of the widest-ranging physical properties in nature.
Quality control in wire and cable manufacturing routinely involves measuring resistance of samples and back-calculating resistivity to verify conductor purity and cross-section. Elongation during drawing can change both geometry and crystal structure, affecting resistivity. IEC 60468 provides standard test methods for resistivity measurement of metallic conductor materials.
This calculator derives resistivity (in units of 10⁻⁸ Ω·m for convenient reading with metals) and conductivity (in 10⁶ S/m) from measured resistance, sample length, and cross-sectional area. It also outputs resistance per metre and total conductance for immediate use in circuit analysis.
All outputs are derived from the fundamental geometry-property relationship:
Cross-sectional area is entered in mm² (the standard unit in cable engineering) and converted internally to m² by multiplying by 10⁻⁶. Results are displayed in scaled units for readability: metals typically have ρ in the range 1–100 × 10⁻⁸ Ω·m.
Compare your calculated resistivity against known reference values: copper ≈ 1.72 × 10⁻⁸ Ω·m, aluminium ≈ 2.82 × 10⁻⁸ Ω·m, gold ≈ 2.44 × 10⁻⁸ Ω·m, iron ≈ 9.7 × 10⁻⁸ Ω·m. A value significantly higher than the expected material ρ suggests impurities, mechanical damage, poor connections, or the wrong material. Conductivity above 5 × 10⁷ S/m indicates a high-purity, high-quality conductor. For IACS comparison, divide σ by 5.8 × 10⁷ and multiply by 100.
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Results
A 100 m long, 1.5 mm² wire with 0.344 Ω resistance gives ρ = 1.72×10⁻⁸ Ω·m — confirming high-purity copper (standard value 1.72×10⁻⁸). Conductivity 5.83×10⁷ S/m ≈ 100.5% IACS.
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Results
ρ = 2.81×10⁻⁸ Ω·m matches aluminium's standard value of 2.82×10⁻⁸ Ω·m — confirming the conductor material is aluminium, approximately 61% IACS.
Resistance (Ω) depends on both the material and the geometry (length, cross-section). Resistivity (Ω·m) is a material constant independent of shape — it is the resistance of a 1 m × 1 m² sample of the material. Resistivity allows fair comparison between different materials.
At 20 °C: Silver 1.59×10⁻⁸, Copper 1.72×10⁻⁸, Gold 2.44×10⁻⁸, Aluminium 2.82×10⁻⁸, Tungsten 5.6×10⁻⁸, Iron 9.7×10⁻⁸ Ω·m. Nichrome: 1.1×10⁻⁶ Ω·m. All values increase with temperature for pure metals.
IACS (International Annealed Copper Standard) defines 100% as the conductivity of annealed copper (5.8×10⁷ S/m). It provides a universal benchmark for comparing conductor materials. Aluminium at ~61% IACS needs a larger cross-section than copper for the same current, but its lower density often makes it preferable for overhead lines.
For metals, resistivity increases with temperature following ρ(T) = ρ₀(1 + α·ΔT). For semiconductors it decreases with temperature. The calculator gives resistivity at the temperature at which the resistance was measured — note the measurement temperature when comparing against reference tables.
Yes — the formula is universal. For carbon composite conductors, electrolytes, conductive polymers, or semiconductors, enter the measured resistance, length, and cross-sectional area and the calculator will correctly compute resistivity. Just note that the displayed units (×10⁻⁸) may not be the most convenient for high-resistivity materials.
Conductance (G = 1/R, measured in siemens S) is the reciprocal of resistance. It is more natural in parallel circuit analysis (parallel conductances add directly: G_total = G₁ + G₂ + …) and in some electromagnetic and electrochemical contexts. High conductance means easy current flow.
The four-wire (Kelvin) measurement method is standard for accurate resistivity determination. Two outer contacts inject current; two inner voltage contacts measure the voltage drop, eliminating contact resistance error. IEC 60468 and ASTM B193 describe the procedure for metallic conductors.
Wire drawing introduces mechanical stress and work-hardening, which increases lattice defects and grain boundary scattering of electrons, raising resistivity. Annealing (heat treatment) restores the original crystal structure and reduces resistivity back toward the bulk value. The IACS standard explicitly specifies annealed copper.
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