Thermal Expansion Calculator

The fundamental linear thermal expansion equation is:

$$\Delta L = \alpha \cdot L_0 \cdot \Delta T$$

where ΔL is the change in length (m), α is the linear coefficient of thermal expansion (/K), L₀ is the original length (m), and ΔT is the temperature change (K).

For two-dimensional and three-dimensional expansion:

$$\Delta A \approx 2\alpha \cdot A_0 \cdot \Delta T$$

$$\Delta V \approx 3\alpha \cdot V_0 \cdot \Delta T = \beta \cdot V_0 \cdot \Delta T$$

where β = 3α is the volumetric expansion coefficient. These are first-order approximations valid for small strains (αΔT ≪ 1), which holds for virtually all engineering scenarios.

The thermal strain ε = αΔT is dimensionless and represents the fractional change in length. If a structure is constrained and cannot expand freely, this strain produces thermal stress σ = EαΔT, where E is the Young's modulus—a critical consideration in structural engineering.

The change in dimension tells you exactly how much a structure grows or shrinks with temperature. For a 100 m steel bridge experiencing a 60 K seasonal temperature swing, the expansion is about 72 mm—this is why expansion joints are essential in bridges, railways, and pipelines.

Materials like Invar (α = 1.2 × 10⁻⁶ /K) were specifically developed for applications requiring dimensional stability, such as precision instruments, clock pendulums, and scientific measurement devices. Aluminum, with α = 23 × 10⁻⁶ /K, expands almost 20 times more than Invar.