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Thermal Expansion Calculator

Find how much a material expands when heated.

How it is calculated

The tool uses linear expansion: ΔL = α × L₀ × ΔT and L = L₀ + ΔL. L₀ is the original length in metres (results are labelled m), α is the coefficient of linear expansion per °C (or per kelvin), and ΔT is the temperature change in °C, positive for heating and negative for cooling. The coefficient is entered as a plain decimal such as 0.000012, not as 12; a value of 12 would be read literally and give an enormous result. Length must be above zero. The new length is shown in metres with six decimals, and so is the expansion unless it is below 0.1 mm: then it is printed in scientific notation, for example 0.01 m with α = 0.000012 and ΔT = 1 gives 1.2000 × 10⁻⁷ m. The formula assumes a uniform material and a small temperature range.

Worked example

A 30 m rail has α = 0.000012 per °C and warms by 50 °C. Step 1: ΔL = 0.000012 × 30 × 50 = 0.018 m. Step 2: new length = 30 + 0.018 = 30.018 m. The tool shows an expansion of 0.018000 m (18 mm) and a new length of 30.018000 m. With a temperature drop of 40 °C instead, ΔL would be −0.0144 m and the rail would shrink.

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Common mistakes

  • Typing the coefficient as 12 when the tabulated value is 12 × 10⁻⁶; enter 0.000012.
  • Mixing °F and °C: a coefficient per °C needs ΔT in °C, and a per-°F coefficient needs ΔT in °F.
  • Entering the final temperature rather than the temperature change; ΔT = final − initial.
  • Entering the length in millimetres or feet; the result is labelled in metres.
  • Applying the linear formula to area or volume; area expansion is about double and volume about triple the linear coefficient.

About this calculator

Linear thermal expansion describes how a material's length changes with temperature: ΔL = α · L₀ · ΔT, where L₀ is the original length, α is the material's coefficient of linear thermal expansion (a property specific to each material, typically expressed per °C or per °F), and ΔT is the temperature change. Most materials expand when heated and contract when cooled because higher thermal energy increases the average distance between atoms in the material's lattice.

Civil and mechanical engineers rely on thermal expansion calculations constantly: bridges include expansion joints, railway tracks are laid with small gaps, and pipelines include expansion loops, all sized using exactly this formula to prevent buckling or cracking as temperatures swing between seasons. It's also essential in manufacturing (fitting a shrink-fit bearing by heating it to expand before assembly), in construction material selection (concrete and steel are chosen partly because their expansion coefficients are similar), and in precision instrument design where even tiny dimensional changes matter.

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Comments (1)

  • Editorial team

    The result is free expansion, what the part would do if nothing held it. If both ends are fixed, it pushes on its supports instead, so expansion gaps are sized from this figure plus a margin. To feel the material effect, 10 m over a 40 °C swing gives 4.8 mm for steel at 0.000012 but 9.2 mm for aluminium at 0.000023. What material and length are you working with?

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