Electrical conductivity and conductor resistance
Electrical conductivity σ describes how readily a material conducts current and is the reciprocal of resistivity ρ. For a uniform conductor with constant cross-section, resistance is length divided by conductivity and area.
Conductivity changes with material composition and temperature. This calculator applies a uniform DC bulk-material model and does not replace conductor tables, standards, or thermal and installation analysis.
How to use the conductivity calculator
- Select the unknown: Choose resistance, conductivity, length, or cross-sectional area.
- Choose units: Select metric or the supported US customary combination.
- Enter positive known values: Provide the other three quantities using the displayed units.
- Calculate and verify: Check temperature, material, geometry, contacts, and AC effects for the real application.
Formula and variables
Use one internally consistent unit system. The calculator converts its supported US customary inputs to SI for calculation and converts the selected output back.
R = L/(σA) = ρL/A- R — Resistance
- End-to-end electrical resistance (Ω)
- σ — Conductivity
- Reciprocal of resistivity (S/m)
- L — Length
- Uniform conductor length (m)
- A — Cross-sectional area
- Uniform area normal to current flow (m²)
Copper-like conductor example
A uniform 10 m conductor has σ = 5.96 × 10⁷ S/m and area 1.0 mm².
- Conductivity
- 5.96 × 10⁷ S/m
- Length
- 10 m
- Area
- 1.0 × 10⁻⁶ m²
- R = 10/(5.96 × 10⁷ × 1.0 × 10⁻⁶)
- R ≈ 0.1678 Ω
Result: The ideal uniform-conductor resistance is approximately 0.168 Ω.
Actual resistance depends on temperature, material condition, connections, and geometry.
Understanding your results
Understand the proportional relationships
Resistance grows with length and falls as conductivity or area increases.
- Doubling length doubles ideal resistance.
- Doubling area halves ideal resistance.
- Conductivity values must correspond to the operating temperature and material.
Assumptions
- The conductor is uniform, isotropic, and has constant cross-sectional area.
- Conductivity is constant along the conductor and at the operating temperature.
- The calculation represents bulk DC resistance.
Limitations
- Does not include contact resistance, temperature rise, joints, tolerances, or material impurities.
- Does not model skin effect, proximity effect, inductance, frequency dependence, or complex conductivity.
- Does not determine safe ampacity, voltage drop under load, or code compliance.
Common mistakes
- Entering mm² as m² without conversion.
- Using room-temperature conductivity at a very different operating temperature.
- Confusing conductivity with resistivity.
- Treating calculated resistance as a wire-ampacity rating.
Practical use cases
Material and geometry comparisons
Compare ideal resistance as conductivity, length, or cross-section changes.
First-pass conductor analysis
Estimate bulk resistance before applying temperature, AC, connection, and safety corrections.
Frequently asked questions
How are conductivity and resistivity related?
For the same homogeneous material model, conductivity is the reciprocal of resistivity: σ = 1/ρ.
Why does copper resistance change with temperature?
Material conductivity is temperature dependent, so use a value or correction appropriate to the operating condition.
Can this calculator select a safe wire size?
No. Safe conductor selection also requires ampacity, insulation, installation, voltage-drop, fault, and applicable-code analysis.
Sources and review
- The International System of Units (SI Brochure) — Bureau International des Poids et Mesures. Accessed 2026-07-13.
Reviewed 2026-07-13.