Thermal Expansion Calculator — Linear and Volumetric
Calculate thermal expansion for solids and liquids. Covers linear expansion ΔL = αLΔT, volumetric expansion, material coefficients, and engineering applications.
Bridges have expansion joints. Railroad tracks are welded with precise gaps. Thermostats use bimetallic strips. All of these rely on the fact that almost every solid expands when heated and contracts when cooled. The amount of expansion depends on temperature change, material properties, and original size.
The CalcHub thermal expansion calculator computes linear and volumetric expansion for any material and temperature change.
The Formulas
Linear expansion: ΔL = α × L₀ × ΔT Volumetric expansion: ΔV = β × V₀ × ΔTWhere β ≈ 3α for isotropic solids.
- α = linear expansion coefficient (per °C or per K)
- β = volumetric expansion coefficient
- L₀, V₀ = original length/volume
- ΔT = temperature change
Coefficients of Linear Expansion
| Material | α (×10⁻⁶ /°C) |
|---|---|
| Steel | 11–13 |
| Aluminum | 23 |
| Copper | 17 |
| Glass (ordinary) | 9 |
| Pyrex glass | 3.3 |
| Concrete | 12 |
| Invar alloy | 1.2 |
| Oak (along grain) | 5 |
Worked Example
A steel bridge span is 200 m long. Temperature ranges from −20°C in winter to +40°C in summer. How much does it expand?
ΔT = 40 − (−20) = 60°C
ΔL = 12 × 10⁻⁶ × 200 × 60 = 0.144 m = 14.4 cm
That's almost 15 cm of expansion over a 200 m span. Expansion joints are sized to accommodate this movement, preventing buckling and fracture.
Why do metals expand when heated?
Atoms in a solid vibrate constantly. Higher temperature means more vibration energy. Due to the asymmetric shape of the interatomic potential energy curve, increased vibration amplitude causes atoms to settle at a larger average separation — the material expands. This is a quantum mechanical effect at its root.
What happens if thermal expansion is constrained?
Enormous thermal stresses develop. Constrained expansion can produce stresses of hundreds of megapascals — enough to crack concrete, buckle rail lines, or fracture glass. This is why glass cookware uses Pyrex (low expansion) and why railways have expansion allowances.
Does water expand when heated?
Water expands with temperature above 4°C — normal behavior. Below 4°C, it does the opposite and expands as it cools toward freezing. This anomalous expansion makes ice less dense than liquid water, which is why ice floats and has enormous ecological importance.