Electrical Resistivity Calculator
Compute the resistance of a conductor from its resistivity, length, and cross-sectional area: R = ρ · L / A. Solve for R, ρ, L, or A — with a live wire diagram, resistance-vs-length chart, material comparison, and step-by-step algebra.
Resistance scales with length
Doubling the length of a wire doubles its resistance, because electrons must travel twice as far and encounter twice as many scattering events. This linear dependence is why long transmission lines lose more power than short ones.
Resistance scales inversely with area
Doubling the cross-sectional area halves the resistance, because twice as many electrons can flow in parallel. This is why thick wires carry more current with less heating — the basis of wire-gauge selection in electrical work.
Resistivity is a material property
The resistivity ρ is intrinsic to the material and independent of geometry. It spans an extraordinary range: 1.6×10⁻⁸ Ω·m for silver to over 10¹⁴ Ω·m for glass — a factor of over 10²². This enormous range is what makes conductors, semiconductors, and insulators distinguishable.
Temperature matters
For metals, resistivity increases roughly linearly with temperature: ρ(T) = ρ₀[1 + α(T − T₀)]. For copper, α ≈ 0.00393 /°C — about 0.4% per °C. This is why motor windings have higher resistance when hot, and why cryogenic cooling dramatically reduces resistance in power cables and MRI magnets.
Resistivity Formulas
For a uniform conductor of constant cross-section.
| Quantity | Formula | Units |
|---|---|---|
| Resistance | R = ρ · L / A | Ω |
| Resistivity | ρ = R · A / L | Ω·m |
| Length | L = R · A / ρ | m |
| Cross-sectional area | A = ρ · L / R | m² |
| Conductance | G = 1/R = σ · A / L | S (siemens) |
| Conductivity | σ = 1/ρ | S/m |
| Temperature correction | ρ(T) = ρ₀[1 + α(T − T₀)] | Ω·m |
| Power dissipated | P = I² · R = V² / R | W |
Resistivity of Common Materials at 20 °C
| Material | ρ (Ω·m) | σ (S/m) | Class |
|---|---|---|---|
| Silver | 1.59 × 10⁻⁸ | 6.30 × 10⁷ | Best conductor |
| Copper | 1.68 × 10⁻⁸ | 5.96 × 10⁷ | Standard conductor |
| Gold | 2.44 × 10⁻⁸ | 4.11 × 10⁷ | Corrosion-resistant contact |
| Aluminum | 2.65 × 10⁻⁸ | 3.77 × 10⁷ | Overhead power lines |
| Tungsten | 5.60 × 10⁻⁸ | 1.79 × 10⁷ | Filaments, electrodes |
| Iron | 9.71 × 10⁻⁸ | 1.03 × 10⁷ | Structural, resistive |
| Platinum | 1.06 × 10⁻⁷ | 9.43 × 10⁶ | Precision RTDs |
| Nichrome | 1.10 × 10⁻⁶ | 9.09 × 10⁵ | Heating elements |
| Carbon (graphite) | 3.5 × 10⁻⁵ | 2.9 × 10⁴ | Resistors, brushes |
| Silicon (pure) | 2.3 × 10³ | 4.3 × 10⁻⁴ | Semiconductor |
| Glass | 10¹¹ – 10¹⁴ | 10⁻¹¹ – 10⁻¹⁴ | Insulator |
| PTFE (Teflon) | 10²² – 10²⁴ | 10⁻²² – 10⁻²⁴ | Best insulator |
Frequently Asked Questions
Resistivity ρ is an intrinsic material property measuring how strongly a material opposes electric current. It is defined as ρ = R·A/L, so a material with ρ = 1 Ω·m produces 1 Ω of resistance in a 1 m long conductor with 1 m² cross-section. Metals have ρ around 10⁻⁸ Ω·m, semiconductors around 10⁻⁵ to 10³ Ω·m, and insulators above 10⁸ Ω·m.
In metals, current is carried by free electrons. As temperature rises, the metal's atoms vibrate more, which increases electron scattering and raises resistivity. For most metals, ρ(T) = ρ₀[1 + α(T − T₀)] with α around 0.004 /°C. Semiconductors behave oppositely — higher temperature releases more charge carriers, so their resistivity decreases.
Silver has the lowest resistivity of any metal (1.59×10⁻⁸ Ω·m vs copper's 1.68×10⁻⁸), but it is far more expensive and less durable. Copper offers an excellent trade-off between conductivity, cost, mechanical strength, and corrosion resistance. Aluminum is cheaper still and lighter, so it is used for overhead power lines, but it has higher resistivity and requires larger cross-sections for the same current.
Resistance R (measured in ohms) depends on both the material and the geometry of the conductor — a long thin copper wire has much higher resistance than a short thick one. Resistivity ρ (measured in Ω·m) is an intrinsic material property that does not depend on geometry. Two copper wires of different sizes have the same resistivity but different resistance. The relation is R = ρ·L/A.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R | Electrical resistance | ohm |
| rho | Electrical resistivity | ohm.m |
| L | Conductor length | m |
| A | Cross-sectional area | m2 |
What it means
Electrical resistivity (ρ, often represented by the Greek letter rho) is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. The resistance R of a uniform conductor is R = ρ L / A, where L is length and A is cross‑sectional area. Resistivity depends on temperature and material purity. Metals have low resistivity (~10⁻⁸ Ω·m), while insulators have very high resistivity. This equation is used in circuit design, power transmission, and selection of materials for heating elements, connectors, and semiconductors. Understanding resistivity is essential for electrical engineering, as it determines power losses, voltage drops, and the design of components like wires and resistors.
Worked example
Electrical Resistivity – Two Examples
Real‑World| Parameter | Value |
|---|---|
| ρ | 1.68×10⁻⁸ Ω·m |
| L | 10 m |
| A | 1×10⁻⁶ m² |
| Parameter | Value |
|---|---|
| ρ | 2.65×10⁻⁸ Ω·m |
| L | 5 m |
| A | 5×10⁻⁷ m² |
Common mistakes
- Electrical resistivity: R = ρ·L/A – resistance of a conductor.
- Resistivity ρ: Material‑specific property – in Ω·m.
- Length L: In metres.
- Cross‑sectional area A: In m² – if using mm², convert appropriately.
- Temperature dependence: ρ changes with temperature – use the value at the operating temperature.
Applications
Electrical resistivity (R = ρ·L/A) relates the resistance of a conductor to its material resistivity, length, and cross‑sectional area. It is fundamental for designing electrical circuits, wiring, and components. Engineers select materials based on resistivity (copper, aluminium for low resistivity; nichrome for high resistivity). Resistivity is also used in eddy current testing for nondestructive evaluation. In materials science, resistivity measurements are used to study phase transformations, alloying effects, and to detect impurities. Understanding resistivity enables efficient power transmission, accurate circuit design, and advanced materials characterization.
- Design of electrical wiring, cables, and connectors
- Selection of conductors and resistors for circuits
- Eddy current testing for defect detection
- Study of phase transformations and precipitation in alloys
- Material purity assessment and quality control
Related calculators · Thermal Properties
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.