What is the resistivity formula?

The resistivity formula is: ρ = R × A / L, where ρ is resistivity in Ω·m, R is resistance in ohms, A is cross-sectional area in m², and L is length in metres. Equivalently, resistance is calculated as R = ρ × L / A. Conductivity σ = 1 / ρ in siemens per metre (S/m).

How does temperature affect resistivity?

For metals, resistivity increases with temperature according to: ρ(T) = ρ₀ × [1 + α × (T − T₀)], where ρ₀ is resistivity at reference temperature T₀ (usually 20 °C), α is the temperature coefficient of resistance (TCR) in 1/°C, and T is the operating temperature. Copper has α ≈ 0.00393 /°C, aluminium ≈ 0.00429 /°C.

What are typical resistivity values for common materials?

At 20 °C: Silver ≈ 1.59×10⁻⁸ Ω·m, Copper ≈ 1.68×10⁻⁸ Ω·m, Aluminium ≈ 2.82×10⁻⁸ Ω·m, Tungsten ≈ 5.60×10⁻⁸ Ω·m, Nickel ≈ 6.99×10⁻⁸ Ω·m, Iron ≈ 1.00×10⁻⁷ Ω·m. Semiconductors like silicon have values around 6.40×10² Ω·m, and insulators like glass can exceed 10¹⁰ Ω·m.

How do I use the bulk resistivity calculator?

For single mode: select calculation type (resistivity from R, or resistance from ρ), enter the required values, and click Calculate. For bulk mode: upload a TXT/CSV with one entry per line in the format: mode,R_or_rho,L,A or paste data directly. Download results as CSV.

Resistivity Calculator

Q: What is electrical resistivity?

Electrical resistivity (ρ, rho) is an intrinsic material property that quantifies how strongly a material opposes the flow of electric current. It is measured in ohm-metres (Ω·m). Unlike resistance, resistivity does not depend on the geometry of the conductor — only on the material itself and its temperature. The formula linking resistance and resistivity is: R = ρ × L / A, where L is the length in metres and A is the cross-sectional area in square metres.

Features

Everything You Need for Resistivity Analysis

From single material lookup to batch conductor design — all in one free tool.

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Live Preview

See resistivity, resistance, and conductivity update in real time as you type — before clicking Calculate.

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Temperature Correction

Apply the temperature coefficient of resistance (TCR) to compute actual resistivity at any operating temperature.

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Bulk CSV/TXT Upload

Process hundreds of material/geometry combinations simultaneously by uploading a plain-text file or pasting data.

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Dual-Mode Calculation

Calculate resistivity from measured resistance, or calculate resistance from known resistivity and geometry.

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Real-Time Validation

Instant input validation catches invalid values, negative dimensions, and physically impossible inputs before calculation.

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Export Results

Download results as CSV, copy to clipboard, or clear and start fresh. Full summary statistics and status badges.

How It Works

Four Steps to Resistivity Calculation

1

Choose Calculation Mode

Select "ρ from R" to derive resistivity from a measured resistance, length, and area. Or select "R from ρ" to compute resistance from known material resistivity and conductor geometry.

2

Enter Geometry & Values

Input conductor length in metres, cross-sectional area in m², and either resistance in ohms or resistivity in Ω·m. The live preview updates instantly.

3

Apply Temperature Correction

Optionally enter operating temperature and material TCR (α) to compute temperature-adjusted resistivity using ρ(T) = ρ₀ × [1 + α × (T − 20)].

4

Export & Use

Download results as CSV or copy to clipboard. For bulk cable or PCB trace analysis, upload a TXT/CSV and process entire design sweeps at once.

Resistivity Calculator: Formula, Examples & Material Reference Guide

Electrical resistivity (ρ, rho) is one of the most fundamental material properties in electronics and electrical engineering. Unlike electrical resistance — which depends on a conductor's shape and size — resistivity is an intrinsic characteristic of the material itself. Understanding how to calculate, apply, and correct resistivity for temperature is essential for designing reliable conductors, PCB traces, cables, and semiconductor devices.

What is Electrical Resistivity?

Resistivity quantifies a material's opposition to electric current flow at the microscopic level. It is measured in ohm-metres (Ω·m). A conductor with low resistivity (like copper at ~1.68 × 10⁻⁸ Ω·m) allows current to pass with minimal energy loss, while an insulator such as glass (ρ > 10¹⁰ Ω·m) almost completely blocks it. Semiconductors occupy the middle ground, with resistivity strongly influenced by doping concentration and temperature.

Key Resistivity Formulas

Resistivity from resistance: ρ = R × A / L
Resistance from resistivity: R = ρ × L / A
Conductivity: σ = 1 / ρ (S/m)
Temperature correction: ρ(T) = ρ₀ × [1 + α × (T − 20)]

Practical Examples

A copper wire 100 m long with cross-section 1.5 mm² (1.5 × 10⁻⁶ m²): R = (1.68 × 10⁻⁸ × 100) / (1.5 × 10⁻⁶) ≈ 1.12 Ω. At 85 °C with α = 0.00393 /°C: ρ(85) = 1.68 × 10⁻⁸ × [1 + 0.00393 × 65] ≈ 2.11 × 10⁻⁸ Ω·m — a 26% increase. This directly affects cable ampacity ratings and voltage drop calculations in power distribution systems.

Usage & Applications

This online resistivity calculator is used by electrical engineers sizing cables and PCB traces, materials scientists characterising thin film conductors, quality control engineers verifying batch material conformance, and electronics students learning conductor physics. The bulk upload feature accelerates design sweeps across multiple conductor cross-sections or temperature operating points without needing MATLAB, Python, or spreadsheets.

FAQ

Frequently Asked Questions

Electrical resistivity (ρ) is an intrinsic material property indicating how strongly a material resists electric current. It is measured in ohm-metres (Ω·m) and is independent of conductor geometry. The formula linking resistance and resistivity is R = ρ × L / A.

ρ = R × A / L, where R is resistance (Ω), A is cross-sectional area (m²), and L is length (m). Conversely, R = ρ × L / A. Conductivity σ = 1 / ρ in siemens per metre (S/m).

For metals, resistivity increases linearly with temperature: ρ(T) = ρ₀ × [1 + α × (T − T₀)], where α is the temperature coefficient of resistance. Copper has α ≈ 0.00393 /°C. Semiconductors show the opposite behaviour — their resistivity decreases as temperature rises.

At 20 °C: Silver ≈ 1.59×10⁻⁸ Ω·m, Copper ≈ 1.68×10⁻⁸ Ω·m, Gold ≈ 2.44×10⁻⁸ Ω·m, Aluminium ≈ 2.82×10⁻⁸ Ω·m, Tungsten ≈ 5.60×10⁻⁸ Ω·m, Iron ≈ 1.00×10⁻⁷ Ω·m. Silicon is around 6.40×10² Ω·m.

Upload a TXT or CSV file with one entry per line. Use format rho,R,L,A to calculate ρ, or res,rho,L,A to calculate R. Optionally append ,T,alpha for temperature correction. You can also paste data directly and click Process Bulk.