Thermal Expansion Calculator

Thermal Expansion Guide

The Formula

Linear expansion: ΔL = α × L₀ × ΔT. Where α is the linear expansion coefficient (per °C), L₀ is original length, ΔT is temperature change. For a 10m steel rail at α = 12×10⁻⁶/°C with ΔT = 50°C: ΔL = 12×10⁻⁶ × 10 × 50 = 0.006m = 6mm. Volumetric expansion coefficient β ≈ 3α for isotropic solids. Water is unusual — it contracts from 0–4°C and expands above 4°C (β = 207×10⁻⁶/°C at 20°C).

Engineering Applications

Railway expansion gaps: rails are left with small gaps (typically 4–6mm per rail length) to accommodate thermal expansion. Road bridge expansion joints serve the same purpose. The Eiffel Tower grows 15–18cm taller in summer vs winter due to thermal expansion of its steel structure. Underground pipes require flexible connectors. Hot water pipes need room to expand in their fixings — overtightened clips cause banging pipes as they expand and contract.

The Bimetallic Strip

A bimetallic strip bonds two metals with different expansion coefficients (often steel α=12 and brass α=19). When heated, the brass expands more than the steel, causing the strip to bend toward the steel side. This is used in thermostats (the bending breaks an electrical circuit when the temperature exceeds a set point), fire sprinklers, and temperature gauges. The greater the temperature change and the greater the coefficient difference, the more the strip bends.

Thermal Stress

When expansion is constrained, thermal stress builds up: σ = E × α × ΔT. Where E is Young's modulus (Pa). For steel (E = 200 GPa) with ΔT = 100°C: σ = 200×10⁹ × 12×10⁻⁶ × 100 = 240 MPa. Steel's yield strength is approximately 250 MPa — meaning constrained heating by 100°C approaches the yield point. This is why unconstrained expansion is critical in structural engineering, and why bridges and pipelines must be designed with expansion accommodation.