How it’s calculated
Most solids grow by a fixed fraction of their length for each degree of temperature rise. The fraction is the coefficient of linear expansion α. For small changes, area grows by about 2α and volume by about 3α per degree.
| Material | α (× 10⁻⁶ /°C) |
|---|---|
| Iron or steel | 12 |
| Concrete, brick | ≈ 12 |
| Copper | 17 |
| Brass | 19 |
| Aluminum | 25 |
| Glass (ordinary) | 9 |
Example (OpenStax University Physics Vol. 2, Example 1.2): the Golden Gate Bridge’s 1275 m steel main span between −15 °C and 40 °C. ΔL = 12 × 10⁻⁶ × 1275 × 55 = 0.84 m.
If expansion is prevented, the member develops stress of about E × α × ΔT instead (e.g. 200 GPa × 12 × 10⁻⁶ × 30 °C ≈ 72 MPa in steel), which is why rails, pipes and bridges need expansion joints or loops.
Frequently asked questions
Does the original temperature matter?
Only through ΔT. α itself varies slightly with temperature, so for large ranges or cryogenic work use temperature-specific data.
Do holes get bigger or smaller when heated?
Bigger. A hole in a plate expands exactly as if it were filled with the same material.
How much does a steel pipe expand?
About 12 mm per 10 m per 100 °C (or roughly 0.8 in per 100 ft per 100 °F).
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Sources
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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