ConverterHub

Linear Thermal Expansion Calculator

Enter the expansion coefficient, original length and temperature change to find ΔL.

How it is calculated

The change in length of a solid bar or rail is ΔL = α × L0 × ΔT, and the new length is L = L0 + ΔL. Here α is the coefficient of linear expansion in 1/°C, written as a plain decimal or in scientific form (0.000012 or 12e-6), L0 is the original length in metres and ΔT is the temperature change in °C: positive for heating, negative for cooling. The tool shows ΔL in metres, the new length in metres with six decimals, and ΔL in millimetres. Very small changes (below 1 mm) are shown in scientific notation such as 1.2000e-4 m. A negative ΔL means the length shrinks. Only L0 must be above zero. The formula treats α as constant, which is a good approximation for moderate temperature ranges only.

Worked example

A steel rail of 100 m with α = 0.000012 per °C is heated by 40 °C. Change in length: ΔL = 0.000012 × 100 × 40 = 0.048000 m, which is 48.00 mm. New length: 100 + 0.048 = 100.048000 m. If the same rail cools by 30 °C instead (ΔT = −30), then ΔL = 0.000012 × 100 × (−30) = −0.036 m: it shortens by 36.00 mm to 99.964000 m.

Try this example →

Common mistakes

  • Typing α as 12 instead of 0.000012 (or 12e-6). The coefficient is per °C, not per million per °C, so a value of 12 makes the rail grow by thousands of metres.
  • Entering the final temperature instead of the temperature change. Enter the difference between the two temperatures, for example 40 for a rise from 10 °C to 50 °C.
  • Entering the length in centimetres or feet while the results are labelled in metres. Use metres for L0, or convert the answer yourself.
  • Dropping the minus sign for cooling. A negative ΔT gives a negative ΔL, meaning shrinkage.
  • Using a coefficient for the wrong material or a volume (cubic) coefficient. This tool needs the linear coefficient, and the volume one is roughly three times as large.

About this calculator

Most solids expand when heated and contract when cooled, and for moderate temperature changes this behavior is well approximated by ΔL = α·L0·ΔT, where α is the material's coefficient of linear thermal expansion — roughly 12×10⁻⁶/°C for steel and 23×10⁻⁶/°C for aluminum, for example.

Engineers rely on this relationship to size expansion joints in bridges, railways, and pipelines, to set clearances in machined assemblies, and to predict the stress that builds up when expansion is mechanically constrained. This calculator is used by mechanical and civil engineers, machinists, and physics students working through thermal expansion problems.

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