# Thermal Expansion Calculator (Linear / Volumetric)

Linear and volumetric thermal expansion of an isotropic material. Linear: ΔL = α·L₀·ΔT, L₁ = L₀·(1+α·ΔT). Volumetric: ΔV = 3α·V₀·ΔT (β = 3α for isotropic solids). Built-in typical α for carbon/alloy steel, aluminum, copper, austenitic stainless, titanium and glass, plus custom. ΔT in K or °C, length in mm, volume in mm³.

> Canonical page: https://elysiatools.com/en/tools/thermal-expansion-calculator

- **Category:** Math & Numbers

- **Keywords:** thermal expansion, linear expansion, volumetric expansion, delta L = alpha·L0·dT, coefficient of expansion, isotropic, heating elongation, mechanical design

## Overview

Calculate linear or volumetric thermal expansion for an isotropic material using its original size, temperature change, and typical or custom linear expansion coefficient. Results include the amount of expansion or contraction and the final length or volume.

## Inputs

- **Mode** (select)
- **Material** (select): Material preset supplies typical linear expansion coefficient α. Choose 'Custom' to enter α.
- **Thermal Expansion α (1/K)** (number): Linear thermal expansion coefficient α in 1/K. Required only when Material is 'Custom'. Typical: steel ≈ 12e-6, aluminum ≈ 23e-6.
- **Original Length L₀ (mm)** (number): Original (unstressed) length in mm. Required in 'linear' mode.
- **Original Volume V₀ (mm³)** (number): Original (unstressed) volume in mm³. Required in 'volumetric' mode.
- **Temperature Change ΔT (K)** (number): Temperature change ΔT in K or °C (same magnitude). Positive = heating (expansion), negative = cooling (contraction).
- **Decimal Places** (number)

## When to use

- Estimate how much a metal rod or other component changes length when heated or cooled.
- Calculate volume changes in isotropic solids such as aluminum blocks or glass components.
- Check thermal movement during mechanical design using standard material coefficients or a custom α value.

## How it works

- Choose Linear or Volumetric mode.
- Select a material preset or choose Custom and enter α in 1/K.
- Enter ΔT in K or °C, then provide the original length in mm or volume in mm³ for the selected mode.
- The calculator applies ΔL = α·L₀·ΔT or ΔV = 3α·V₀·ΔT and returns the change and final value as JSON.

## Use cases

- Mechanical design checks for rods, rails, shafts, and other components exposed to temperature changes.
- Thermal clearance estimates for aluminum, steel, copper, stainless steel, titanium, glass, and custom materials.
- Volume change calculations for isotropic solid parts during heating or cooling.

## Frequently asked questions

### What is the difference between linear and volumetric expansion?

Linear expansion calculates a change in length, while volumetric expansion calculates a change in volume for an isotropic material.

### Which units should I use?

Enter length in mm, volume in mm³, and temperature change in K or °C. Kelvin and Celsius temperature differences have the same numerical value.

### What does a positive ΔT mean?

A positive ΔT represents heating and produces expansion. A negative ΔT represents cooling and produces contraction.

### Can I enter my own thermal expansion coefficient?

Yes. Select Custom for the material and enter the linear coefficient α in 1/K.

### How is volumetric expansion calculated?

For an isotropic solid, the calculator uses ΔV = 3α·V₀·ΔT, where the volumetric coefficient β equals 3α.

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