Thermal Expansion Calculator
Enter the length, the material's expansion coefficient and the start and end temperatures. You get the change in length and the new length.
Typical values only. Grades vary, so check the supplier's data for a real design.
Worked examples
Steel beam
10 m, coefficient 12e-6, 20 C to 70 C
6 mm longer
12e-6 x 10 x 50.
Aluminium bar
1 m, 23.1e-6, 0 C to 100 C
2.31 mm longer
23.1e-6 x 1 x 100.
About Thermal Expansion Calculator
Most materials expand when they get hotter and shrink when they cool. For a bar, the change in length is the original length multiplied by the coefficient of linear expansion, multiplied by the change in temperature. The effect is small but adds up over long lengths: a 10 metre steel beam warmed by 50 degrees grows by 6 millimetres. That is why bridges have expansion joints and rails are laid with gaps or tensioned.
Different materials expand by different amounts, which matters wherever they are joined. Aluminium expands about twice as much as steel, so an aluminium frame on a steel base can bind or loosen with the weather. Pick a material from the menu to fill in a typical coefficient, or type your own. The page also shows the area and volume expansion, which are approximately two and three times the linear figure.
How to use Thermal Expansion Calculator
- Enter the original length and choose the unit.
- Pick a material from the menu or type the coefficient of linear expansion.
- Enter the starting and final temperatures in degrees Celsius.
- Read the change in length and the new length.
Common uses
- Leaving gaps for expansion in fences, decking and pipework
- Estimating the growth of a long metal run in summer
- Checking tolerances for parts joined from different metals
- Physics and engineering coursework
Frequently asked questions
What is the thermal expansion formula?
Change in length = alpha x L x delta T, where alpha is the coefficient of linear expansion per kelvin, L the original length and delta T the temperature change.
What is the coefficient for steel?
About 12 x 10 to the minus 6 per kelvin for carbon steel, 17 for stainless steel, 23 for aluminium and 16.5 for copper. Exact grades vary.
How does area or volume expand?
Area expands by about twice the linear fraction, and volume by about three times, for small changes in temperature.
Do plastics expand more than metals?
Generally yes, often five times as much as steel or more. Check the data for the plastic you use.