About this tool
The Thermal Expansion Calculator works out how much a part grows or shrinks with a change in temperature, and optionally the stress that builds up if the part is held rigidly and cannot expand. Choose a material — or type a custom coefficient — select whether you are expanding a length, an area or a volume, enter the original size and the temperature change, and it returns the dimensional change and the new size. It runs entirely in your browser.
Linear expansion follows ΔL = α·L₀·ΔT, giving a new length L₀·(1 + α·ΔT), where α is the linear coefficient of thermal expansion. Area expansion uses approximately 2α and volumetric expansion 3α, so the tool multiplies the linear strain by 1, 2 or 3 for the dimension type you pick. The built-in coefficients are in units of 10⁻⁶ per °C: steel 12, cast iron 11, stainless 17, aluminium 23, copper 17, brass 19, titanium 8.6, concrete 12, glass 9 and PVC 50. Temperature change can be entered in °C or °F (a delta of °F is scaled by 5/9). If you supply an elastic modulus, the fully constrained thermal stress is σ = E·α·ΔT, reported in MPa and psi.
As a worked example, a 1000 mm steel bar heated by 80 °C expands by 12 × 10⁻⁶ × 1000 × 80 = 0.96 mm, reaching 1000.96 mm. If that same bar were rigidly clamped so it could not grow, the compressive thermal stress with E = 200 GPa would be 200,000 × 12 × 10⁻⁶ × 80 ≈ 192 MPa — which is why bridges, rails and pipework need expansion joints and loops to relieve exactly this stress.