Thermal Expansion Calculator

The coefficient of thermal expansion describes how much a material's size changes per degree of temperature change. The linear coefficient ($\alpha$) applies to length, and the volumetric coefficient ($\beta$) applies to volume. For steel, $\alpha \approx 12 \times 10^{-6}$ /K, meaning it expands 12 micrometers per meter for each degree Celsius rise.

Bridge decks can expand several centimeters between winter and summer temperatures. A 100-meter steel bridge experiencing a 50 K temperature swing would expand about 60 mm. Expansion joints provide a controlled gap that absorbs this movement, preventing structural damage.

For isotropic materials, the volumetric coefficient $\beta$ is approximately three times the linear coefficient $\alpha$ ($\beta \approx 3\alpha$). This is because volume scales as the cube of linear dimension. For a cube with side $L$, volume $V = L^3$, so a small change $dL$ gives $dV = 3L^2 dL = 3V (dL/L) = 3V \alpha \Delta T$, hence $\beta = 3\alpha$.

Most do, but there are notable exceptions. Some ceramics like cordierite and certain glasses (Zerodur) have near-zero expansion. Materials like zirconium tungstate and some metal-organic frameworks have negative thermal expansion — they shrink when heated. Water between 0°C and 4°C also exhibits anomalous negative expansion.

If a material is prevented from expanding, internal stress develops instead of dimensional change: $\sigma = E \cdot \alpha \cdot \Delta T$, where $E$ is Young's modulus. A steel beam prevented from expanding under a 50 K temperature rise develops about 120 MPa of compressive stress — enough to buckle slender members.