Science · 47 calculators
Thermal Expansion Calculator
Most materials get longer as they get warmer. The change is small, predictable, and large enough to buckle a bridge or jam a piston if nobody allowed for it.
Change in length
0.0048
- Final length
- 10.0048
- Strain
- 4.80%
- Area change
- 9.60%
- Expansion per degree
- 0.0001
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
delta L = alpha x L x delta T
- dL
- The change in length, positive when the material warms
- alpha
- The coefficient of linear expansion, how much a unit length grows per degree
- L
- The original length
- dT
- The change in temperature, negative for cooling
How to check the result by hand
- 1
Find the coefficient for the material
Look up the coefficient of linear expansion, usually quoted per million per degree. Steel is about 12, aluminium about 23 and concrete about 10.
- 2
Convert it out of per million
Divide by a million before using it. Twelve per million becomes 0.000012 per degree, which is the value the formula expects.
- 3
Multiply by the original length
Ten metres times 0.000012 gives 0.00012 metres of growth per degree of warming.
- 4
Multiply by the temperature change
A rise of 40 degrees gives 0.0048 metres. The final length is 10.0048 metres.
- 5
Check the scale before dismissing it
Four point eight millimetres over ten metres is a strain of 0.048 percent. Over a hundred metre structure the same conditions give 48 millimetres, which is why long spans need joints.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Thermal Expansion page.