Thermodynamics · Materials
Thermal Expansion Calculator
Size linear growth from temperature — pick a solve mode, drop in length and ΔT, and watch the bar diagram stretch as your numbers land.
Result
Linear expansion
ΔL = α · L₀ · ΔT
Enter original length and temperature change to see ΔL animate on the bar diagram.
Reference notes for linear expansion — the mode this calculator solves.
Heating increases molecular vibration and average spacing, so solids, liquids, and gases change size. For small temperature swings, linear expansion stays proportional to original length, coefficient α, and temperature change ΔT.
- Linear expansionΔL = α · L₀ · ΔT
- New lengthL = L₀ · (1 + α · ΔT)
- Required ΔTΔT = ΔL / (α · L₀)
- Coefficientα = ΔL / (L₀ · ΔT)
- Area (approx.)ΔA ≈ 2α · A₀ · ΔT
- Volume (approx.)ΔV ≈ 3α · V₀ · ΔT
| Material | µm/(m·K) | Notes |
|---|---|---|
| Aluminum | 23.1 | High expansion — heat sinks, extrusions |
| Steel (carbon) | 11.7 | Structural frames and machinery |
| Copper | 16.5 | Bus bars and heat transfer |
| Borosilicate glass | 3.3 | Labware, low thermal shock risk |
| Concrete | 12.0 | Why expansion joints exist in slabs |
| Invar (36% Ni-Fe) | 1.2 | Precision instruments, optics beds |
| Titanium | 8.6 | Aerospace and biomedical |
| PVC | 52.0 | Plumbing runs need slack |
Expansion joints
Let bridges and façades breathe without crushing bearings.
Bimetallic strips
Thermostats bend when two metals expand differently.
Shrink fits
Heat the outer part, assemble cold, lock on cooldown.
Thermal stress
Constrained growth becomes stress — watch fixed ends.
Piping
Loops and bellows absorb axial growth in hot lines.
Metrology
Low-α alloys keep gauges stable across shop temperatures.
- The Eiffel Tower grows up to ~15 cm taller on hot summer days.
- Rail gaps prevent track buckling when steel rails heat up.
- Dental fillings must match tooth CTE to avoid micro-cracks.
- Water is densest at 4 °C — ice expands because of hydrogen bonding.
- Engine clearances are sized for hot-running dimensions, not cold assembly.
- A tight jar lid often loosens after a quick hot-water soak — expansion at work.