The formula
ΔL = α · L₀ · ΔT
| Symbol | Quantity | Unit |
|---|---|---|
| ΔL | Change in length | m |
| a | Coefficient of expansion | 1/K |
| L₀ | Initial length | m |
| ΔT | Change in temperature | K |
What it means
Most materials expand when heated because their atoms vibrate more and sit further apart on average. The coefficient of linear expansion says how much per degree, per unit of original length.
How to work it out by hand
- Multiply the coefficient by the original length
- Multiply by the temperature change
- The result is the change in length
What is worth knowing
The numbers look negligible and are not. Steel expands about 12 millionths per degree, so a 100-metre bridge span moves about 5 cm across a 40-degree annual range — which is why expansion joints exist and why railway track used to be laid with gaps. Concrete and steel happen to have almost identical coefficients, and reinforced concrete depends entirely on that coincidence: if they differed much, the steel would tear itself out of the concrete with every temperature cycle. Water is the exception again, contracting as it warms from 0 to 4 °C.