Linear Thermal Expansion Calculator
Find how much a rod, rail or pipe lengthens when heated, from its length, temperature change and expansion coefficient.
How it works
ΔL = α · L₀ · ΔT · L = L₀ + ΔL
Most solids expand when heated because the atoms vibrate with greater amplitude and sit slightly farther apart on average. The change in length is proportional to the original length, the temperature change, and the material’s linear expansion coefficient α (per °C). Even small α values matter over long spans, which is why bridges and rails include expansion joints.
Worked example
A 10 m steel rail (α = 12×10⁻⁶ /°C) warmed by 40 °C grows by ΔL = 12×10⁻⁶ × 10 × 40 = 0.0048 m = 4.8 mm.
Sources: Thermal expansion — Wikipedia
Frequently asked questions
What is the linear expansion coefficient?
It is the fractional change in length per degree of temperature change, symbol α, with units of 1/°C. Steel is about 12×10⁻⁶, aluminium about 23×10⁻⁶, so aluminium expands nearly twice as much for the same heating.
Why do bridges have expansion joints?
A long steel span can lengthen by centimetres between winter and summer. Expansion joints and gaps let the structure grow and shrink without buckling or cracking.
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This calculator is for educational purposes. Double-check important results before acting on them.