Why materials expand
When a material warms up, its atoms vibrate more and move slightly apart, so it lengthens; when it cools, it shrinks. The effect is small but adds up over long lengths and large temperature swings, which is why bridges have expansion joints, railroads use pre-stressed welded rail, and plumbers add loops or expansion couplings to long pipe runs.
The formula
ΔL = α × L × ΔT
- α: the coefficient of linear expansion, in millionths per °C (10⁻⁶/°C)
- L: the original length
- ΔT: the temperature change, in °C (1 °C = 1.8 °F)
For volume, the coefficient is about 3 × α for solids that expand equally in every direction. The calculator shows the change in length, the final length and the volume change.
Common coefficients
| Material | α (10⁻⁶/°C) |
|---|---|
| Wood along the grain | 3–5 |
| Glass | 9 |
| Concrete | 10–12 |
| Carbon steel | 12 |
| Copper | 16.5 |
| Stainless steel | 17.3 |
| Brass | 19 |
| Aluminum | 23.1 |
| PVC | 50–54 |
Worked example
A 100 ft steel pipe installed at 30 °F heats to 100 °F, a rise of 70 °F or 38.9 °C.
ΔL = 0.000012 × 100 ft × 38.9 = 0.0467 ft ≈ 0.56 inch (14.2 mm).
The same run in PVC would grow about 2.4 inches, more than four times as much, enough to bow the pipe or crack a fitting if it is clamped rigidly.
Practical consequences
- Concrete slabs and sidewalks get control and expansion joints every few feet.
- Vinyl siding must hang loosely on its nails, with gaps at the ends, or it buckles in the sun.
- Hot-water pipes in long straight runs need expansion loops or offsets.
- Steel bridges use sliding bearings and finger joints that open and close with the seasons.
- Lids stuck on jars loosen under hot water because the metal lid expands more than the glass.
Limits
The coefficient varies slightly with temperature, and composites, wood across the grain and some plastics expand differently in different directions. For engineering design, use the manufacturer’s data for your material and temperature range.