Thermal Expansion Calculator
Find how much a part grows or shrinks with temperature using ΔL = α · L₀ · ΔT.
ΔL = α × L₀ × ΔT = 0.006 m. Final length = 10.006 m (ΔT = 50 °C).
Linear thermal expansion is ΔL = α · L₀ · ΔT — the expansion coefficient times the original length times the temperature change. A 10 m steel beam (α = 12×10⁻⁶ /°C) warmed by 50 °C grows ΔL = 12×10⁻⁶ × 10 × 50 = 0.006 m = 6 mm, so its final length is 10.006 m.
Why materials expand when heated
Heating a solid makes its atoms vibrate harder and sit a little farther apart, so the whole object grows; cooling reverses it. The coefficient of linear thermal expansion (α) captures how strongly a given material responds — it is the fractional change in length per degree, so its units are per °C (identical in size to per kelvin, since a one-degree change is the same on both scales). Metals like aluminum expand a lot; special alloys like Invar barely move at all.
Expansion happens in every direction. Linear expansion tracks one dimension (length). Area expansion tracks a surface and grows with a coefficient of roughly 2α, while volumetric expansion tracks the whole solid with roughly 3α. Those factors of 2 and 3 come straight from squaring and cubing a length that has each grown by the same small fraction.
ΔL = change in length (m), α = linear expansion coefficient (per °C), L₀ = original length (m), ΔT = temperature change (°C)
Worked example
A 10 m mild-steel beam (α = 12×10⁻⁶ /°C) heats from 20 °C to 70 °C. Find how much it lengthens and its final length.
- 1 Look up the expansion coefficient. Mild steel has α = 12×10⁻⁶ /°C — a fractional stretch of 0.000012 per degree.
- 2 Find the temperature change ΔT. ΔT = 70 °C − 20 °C = 50 °C. A ΔT in °C equals the same ΔT in kelvin.
- 3 Apply ΔL = α · L₀ · ΔT. ΔL = 12×10⁻⁶ × 10 m × 50 °C = 0.006 m = 6 mm.
- 4 Add it to the original length. L = L₀ + ΔL = 10 + 0.006 = 10.006 m.
- 5 Scale up for area or volume if needed. Area change ≈ 2αΔT and volume change ≈ 3αΔT, here 0.12% and 0.18% of the original.
Linear expansion coefficients (α)
Typical values near room temperature, in ×10⁻⁶ per °C. Values vary a little with grade and temperature range.
| Material | α (×10⁻⁶ /°C) | Note |
|---|---|---|
| Aluminum | 23 | Expands the most of the common metals |
| Gold | 14 | Soft, dense metal |
| Copper | 17 | Common in pipes and wiring |
| Stainless steel | 17 | Higher than mild steel |
| Steel (mild) | 12 | Reference structural value |
| Iron | 12 | Similar to mild steel |
| Concrete | 12 | Close to steel — why reinforcement works |
| Glass (ordinary) | 9 | Low; borosilicate is lower still |
| Invar | 1.2 | Nickel–iron alloy made to barely expand |
Where this matters: expansion joints and rail gaps
Because a long structure can move by millimetres or centimetres across a hot summer day, engineers design the movement in rather than fight it. Bridges sit on expansion joints and sliding bearings so the deck can grow without buckling or cracking its supports. Railway tracks traditionally left small gaps between rails — the source of the classic clickety-clack — and modern continuous welded rail is instead pre-stressed and heavily anchored so it cannot buckle. Pipelines use expansion loops for the same reason.
Matched coefficients matter too: reinforced concrete works partly because steel and concrete expand at almost the same rate (both about 12×10⁻⁶ /°C), so they stay bonded through temperature swings. When two joined materials have very different coefficients — a reason Invar exists — the mismatch shows up as warping (a bimetallic strip) or cracking.