How to use this calculator
- Enter or choose expansion type.
- Enter or choose original size.
- Enter or choose expansion coefficient.
- Enter or choose initial temperature.
- Enter or choose final temperature.
- The change in size updates as you type. Use Copy result or Share to keep it.
Method
ΔL = α × L₀ × ΔT; ΔV = β × V₀ × ΔT; final size = original + change
- α, β
- linear or volumetric expansion coefficient, per kelvin
- L₀, V₀
- original length or volume
- ΔT
- final minus initial temperature
Worked example
- ΔT = 50 − 20 = 30 K.
- ΔL = 12 × 10⁻⁶ × 10 000 mm × 30 = 3.6 mm.
- Final length = 10 000 + 3.6 = 10 003.6 mm (0.036% longer).
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.