What is the formula for linear thermal expansion?

ΔL = α · L₀ · ΔT, where α is the linear coefficient of thermal expansion (per °C or per K), L₀ is the original length, and ΔT is the temperature change. The final length is L = L₀ + ΔL.

What is the difference between linear and volumetric expansion?

Linear expansion measures the change in one dimension (length). Volumetric expansion measures the change in three dimensions (volume). For isotropic materials, the volumetric coefficient β ≈ 3α.

What units does the calculator use for the coefficient?

The coefficient of thermal expansion is expressed in 1/°C (or equivalently 1/K, since a degree Celsius and a kelvin are the same size). You can enter temperature change in either °C or °F — the calculator converts automatically.

Why is my result negative?

A negative result means the material contracted. This happens when ΔT is negative (i.e., the material was cooled below its initial temperature).

How accurate are the preset material coefficients?

The presets use commonly cited engineering reference values at room temperature. Real-world coefficients vary slightly with temperature range, alloy composition, and manufacturing process. For precision work, use a verified datasheet value via the custom input.

Thermal Expansion Calculator

Name: Thermal Expansion Calculator
Availability: InStock
Author: Nham Vu

Calculate how much a material expands or contracts due to temperature change using linear or volumetric expansion formulas.

Inputs

Expansion Type

Initial Length (L₀)

Temperature Change (ΔT)

Material Preset

Coefficient α (linear) or β (volumetric) — per °C

× 1 /°C

Select a preset or enter a value (e.g. 11.7e-6 for steel).

Enter values and click Calculate to see results.

Summary

Calculate how much a material expands or contracts due to temperature change using linear or volumetric expansion formulas.

How it works

Choose between Linear (length) or Volumetric (volume) expansion mode.
Enter the initial length or volume with the appropriate unit.
Enter the temperature change (positive = heating, negative = cooling).
Select a preset material or enter a custom expansion coefficient.
Click Calculate to see the expanded/contracted dimension and the change amount.

Use cases

Estimate gap allowances for steel rails, bridges, and pipelines.
Determine thermal stress in mechanical assemblies and joints.
Check expansion of plastic or rubber components in hot environments.
Verify liquid overflow when heating fluids in closed containers.
Classroom and lab calculations for physics and materials science.
Validate engineering tolerances for precision parts across temperature ranges.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu