# Thermal Expansion Calculator

> Calculate how much a rod, pipe, rail or volume of liquid grows or shrinks with temperature, from its expansion coefficient and temperature change.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/thermal-expansion-calculator

Most materials grow in proportion to their size and the temperature rise: ΔL = αL₀ΔT for length, ΔV = βV₀ΔT for volume.

Also called: Linear expansion calculator, Volume expansion calculator.

## Inputs
- Expansion type (options: Linear (length), Volumetric; default linear)
- Original size (default 10000)
- Expansion coefficient (unit × 10⁻⁶ /K; default 12)
- Initial temperature (unit °C; default 20)
- Final temperature (unit °C; default 50)

## Results
- Change in size
- Final size
- Relative change
- Thermal strain

## Formula

```
ΔL = α × L₀ × ΔT;  ΔV = β × V₀ × ΔT;  final size = original + change
```

Where:
- α, β: linear or volumetric expansion coefficient, per kelvin
- L₀, V₀: original length or volume
- ΔT: final minus initial temperature

## Worked example
1. ΔT = 50 − 20 = 30 K.
2. ΔL = 12 × 10⁻⁶ × 10 000 mm × 30 = 3.6 mm.
3. Final length = 10 000 + 3.6 = 10 003.6 mm (0.036% longer).

**Result:** A 10 m steel member warmed by 30 K grows by 3.6 mm.

## What the result means

Restrained members cannot grow freely, so the same strain turns into stress. That is why pipes have expansion loops and bridges have expansion joints.

## Assumptions and limits
- The coefficient is constant over the temperature range.
- The object can expand freely.
- Water is anomalous below 4 °C and its β changes strongly with temperature; use β at the mean temperature.
- Not valid across phase changes.

## Questions

### How are α and β related?

For an isotropic solid, β ≈ 3α. Liquids have only a volumetric coefficient.

### What does “× 10⁻⁶ /K” mean?

Micrometres of growth per metre of length per kelvin. Steel at 12 grows 12 µm per metre for each degree.

## Related calculators
- [Heat Capacity Calculator](https://calculators.geekmidst.com/calculators/heat-capacity-calculator)
- [Length Converter](https://calculators.geekmidst.com/calculators/length-converter)
- [Temperature Converter](https://calculators.geekmidst.com/calculators/temperature-converter)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/thermal-expansion-calculator