Thermal Expansion Calculator
Linear and volume thermal expansion of solids and liquids.
About this tool
Choose length of a solid, volume of a liquid or volume of a solid, pick a material (or type a coefficient), and enter the original size and temperatures. The tool shows the change, the new size and the percentage change.
How much things expand
Heating makes atoms vibrate more and sit slightly further apart, so most materials expand. For length, ΔL = α × L × ΔT, where α is the linear expansion coefficient; for volume, ΔV = β × V × ΔT, and for solids β is about 3α. Steel's α is about 12 × 10⁻⁶ per °C, so a 100 m steel bridge grows about 4.8 cm between 0 °C and 40 °C. That's why bridges have expansion joints and railways leave gaps or pre-stress the rails. Aluminium (23 × 10⁻⁶) expands about twice as much as steel and PVC more than four times, while borosilicate glass and the alloy Invar barely change, which is why they're used in ovenware and precision instruments. Liquids expand more: 1,000 L of petrol warmed by 20 °C gains about 19 L, one reason fuel is sold by volume at a reference temperature in some countries. Honest limits: coefficients are typical room-temperature values that vary with alloy and temperature, and water is unusual because it contracts between 0 and 4 °C. The specific heat calculator and the density calculator are related.
Frequently asked questions
What is the formula for thermal expansion?
Linear: ΔL = α × L × ΔT. Volume: ΔV = β × V × ΔT, with β about 3α for solids.
How much does steel expand?
About 12 millionths of its length per °C: a 10 m steel beam grows 1.2 mm for a 10 °C rise.
Which materials expand the least?
Invar, fused silica and borosilicate glass have very low expansion coefficients.
Why do bridges have expansion joints?
So the deck can lengthen and shorten with temperature without cracking or buckling.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.