Linear Thermal Expansion

The engineering

Metals grow with heat at parts-per-million rates that feel negligible until length or precision multiplies them: a 30 m steel bridge span swings ~25 mm across a 70 °C seasonal range, and a 300 mm aluminum optical bench drifts 7 µm per degree — a whole wavelength of red light. Expansion joints, slotted holes, and Invar exist because someone once didn't do this multiplication.

The number that bites hardest is *differential* expansion: bolt aluminum to steel and every degree of swing loads the joint with an 11 µε/°C strain fight. Constrained expansion converts directly to stress — σ = EαΔT — and for steel that's about 2.4 MPa per °C, which is how a fully-restrained pipe run buckles itself on a sunny afternoon.

Where this math comes from

Thermal expansion became quantitative when clocks demanded it: John Harrison's 1726 gridiron pendulum stacked brass and steel rods so their opposing expansions cancelled, keeping pendulum length — and time — constant through the seasons. Lavoisier and Laplace measured expansion coefficients systematically with their dilatometer in the 1780s, turning a nuisance into tabulated data.

The virtuoso ending belongs to Charles-Édouard Guillaume, who in 1896 discovered that a 36% nickel-iron alloy — Invar, for 'invariable' — barely expands at all. It rescued precision surveying and horology at a stroke and won him the 1920 Nobel Prize in Physics, still the only Nobel awarded essentially for a thermal-expansion coefficient.

1. 1726John HarrisonGridiron pendulum cancels expansion with brass against steel.
2. 1782Lavoisier & Laplace (circa)Systematic dilatometer measurements of expansion coefficients.
3. 1896Charles-Édouard GuillaumeInvar discovered — near-zero expansion alloy.
4. 1920Charles-Édouard GuillaumeNobel Prize for Invar and precision metrology.

See the full timeline of the math behind every calculator →

Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.