Thermal expansion formula
Most materials grow when heated. The linear thermal expansion formula gives that change in length from the expansion coefficient, the original length, and the temperature change, which is essential for sizing gaps and joints.
Variables
| ΔL | Change in length | m or in |
| α | Coefficient of thermal expansion | per °C or per °F |
| L | Original length | m or in |
| ΔT | Temperature change | °C or °F |
Rearranged
Required gap: ΔL = α × L × ΔT
Worked example
A 10 m steel beam (α = 12 × 10⁻⁶ per °C) warms by 40 degrees.
Multiply through: 12×10⁻⁶ × 10 × 40 = 0.0048 m.
This is linear expansion, the change along one dimension. Area expands at about twice the linear rate and volume at about three times. Because long members move noticeably with temperature, bridges, rails, and pipework include expansion joints to absorb the growth without buckling.
Need expansion coefficients?
See the Thermal Expansion Coefficients chart for common materials.
Linear, area, and volume expansion
The coefficient of linear expansion governs change in length. For the same material, area grows at roughly twice that coefficient and volume at roughly three times, since each adds another expanding dimension. This is why a heated plate grows in both directions and a heated block swells throughout, all traceable to the single linear coefficient.
Why expansion joints exist
A restrained member that cannot expand develops large thermal stresses instead, enough to buckle rails or crack concrete. Expansion joints, sliding bearings, and loops in pipework give the material room to move so the growth is taken up harmlessly. The expected movement comes straight from this formula, using the temperature range the structure will see.
FAQ
What is the thermal expansion formula?
Change in length equals the expansion coefficient times the original length times the temperature change, delta L = alpha L delta T.
How much does steel expand?
About 12 microns per metre per degree C. A 10 m steel beam grows roughly 4.8 mm over a 40 degree rise.
How do area and volume expansion compare?
Area expands at about twice the linear coefficient and volume at about three times, since each adds another expanding dimension.