Resistivity Calculator

Calculate resistivity, resistance, length or cross‑section using ρ = R·A / L. Includes temperature coefficient and material reference.

Fundamental relation: R = ρ · L / A   or   ρ = R · A / L

where R = resistance (Ω), ρ = resistivity (Ω·m), L = length (m), A = cross‑section (m²).

Note: Thermal expansion of length/area is negligible for most applications (typically < 0.002% per °C).
Copper (20°C) Aluminum Silver Gold Nichrome
Calculation Result
1.724e-8 Ω·m
Resistivity (SI)
1.724e-8 Ω·m
Resistance (Ω)
0.1724
Length (m)
10.0
Area (m²)
1.0e-6
ρ = R·A/L = 1.724e-8 Ω·m

Resistance vs. Length (for current ρ and A)

Understanding Resistivity

Resistivity (ρ) is a fundamental property of a material that quantifies how strongly it opposes electric current. It is defined by the equation:

ρ = R · A / L   where R = resistance, A = cross‑section, L = length.

The SI unit is ohm‑meter (Ω·m). Good conductors (copper, silver) have very low resistivity (≈10⁻⁸ Ω·m), while insulators (glass, rubber) exceed 10¹⁰ Ω·m.

Microscopic Origin

Resistivity arises from collisions between conduction electrons and lattice atoms. It depends on:

  • Material structure: crystalline vs. amorphous.
  • Temperature: higher temperature → more lattice vibrations → higher resistivity (positive α for metals).
  • Impurities and defects: increase resistivity.

Temperature Dependence

For most metals, resistivity increases linearly with temperature over a limited range:

ρ(T) = ρ₀ · [1 + α · (T – T₀)]

where α is the temperature coefficient (1/°C). This calculator applies the same correction to resistance (since R ∝ ρ). Thermal expansion of length and area is typically ignored (≤ 0.002%/°C).

Common Material Resistivities (at 20°C)

Material ρ (Ω·m) α (1/°C) Application
Silver 1.59×10⁻⁸ 0.0038 High‑frequency contacts
Copper 1.724×10⁻⁸ 0.00393 Wiring, cables
Gold 2.44×10⁻⁸ 0.0034 Corrosion‑resistant contacts
Aluminum 2.65×10⁻⁸ 0.00429 Power lines
Iron 9.7×10⁻⁸ 0.0050 Structural, transformers
Nichrome (NiCr) 1.0×10⁻⁶ 0.0004 Heating elements
Carbon (graphite) 3.5×10⁻⁵ -0.0005 Brushes, resistors

Practical Applications

1
Wire sizing: Determine required cross‑section to keep voltage drop below a limit.
2
Fault current analysis: Resistance of conductors affects short‑circuit current.
3
Temperature sensing (RTD): Platinum resistance vs. temperature (α ≈ 0.00385).

Design Tip: Always use the same units consistently. This calculator automatically converts all inputs to SI (meter, m², Ω) before computing, then displays results in your preferred unit.

Unit note: 1 circular mil = area of 1 mil diameter circle ≈ 5.067×10⁻¹⁰ m² (exact: π/4 × (0.0254 mm)²).

Frequently Asked Questions

Resistance (R) is a property of a specific object (depends on geometry). Resistivity (ρ) is a material property, independent of shape.

Lattice vibrations (phonons) increase, scattering electrons more effectively. In semiconductors, resistivity usually decreases because more carriers are excited.

A circular mil is a unit of area used in North America for wire cross‑section. 1 circular mil = area of a circle with diameter 1 mil (0.001 in). Exact conversion: 1 circmil = π/4 × (0.0254 mm)² = 5.06707479×10⁻¹⁰ m².