Thermal Expansion Calculator

Most materials expand when heated and contract when cooled, and the size of that change matters in any engineering or construction context where parts must fit together across a range of temperatures. This calculator handles both linear thermal expansion, which describes how much a length changes, and volumetric thermal expansion, which describes how much a volume changes. For linear expansion, the governing formula is delta L = alpha times L0 times delta T, where alpha is the coefficient of linear thermal expansion for the material in units of per degree Celsius or per kelvin, L0 is the original length, and delta T is the temperature change. A positive delta T means heating and a positive delta L means the object gets longer. For volumetric expansion, the formula is the same in form but uses the volumetric coefficient beta, which for an isotropic solid is approximately three times the linear coefficient. You choose the expansion type, enter the original dimension, the expansion coefficient, and the temperature change, and the calculator returns the change in length or volume, the final dimension, and the thermal strain as a dimensionless fraction. Common material presets are included to make it easier to get started. The results are suitable for preliminary engineering planning, science experiments, and educational use. For structural design with large temperature swings or critical tolerances, always consult material data sheets and relevant standards.

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m
/°C
°C
0.012 m
change in length (delta L)
In mm12 mm
Final length10.012 m
Thermal strain1.2000e-3

Coefficients are for room-temperature reference; they vary slightly with temperature. For precision applications verify against certified material data.

How it works

For linear expansion: ΔL = α × L0 × ΔT, where α is the linear coefficient in /°C, L0 is the original length in metres, and ΔT is the temperature change in degrees Celsius. Final length = L0 + ΔL. Thermal strain = ΔL / L0 = α × ΔT. For volumetric expansion: ΔV = β × V0 × ΔT, where β ≈ 3α for isotropic solids. Results are shown in the same units as the input dimension.

Worked example

A steel rail is 10 m long at a reference temperature. Steel has a linear expansion coefficient of 12 × 10-6 per °C (0.000012 /°C). On a hot day the temperature rises by 100 °C. Delta L = 0.000012 × 10 × 100 = 0.012 m (12 mm). The final length is 10.012 m and the thermal strain is 0.0012. These match the default values pre-filled in the calculator above.

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Frequently asked questions

What is the formula for linear thermal expansion?

The formula for linear thermal expansion is delta L = alpha times L0 times delta T, where delta L is the change in length, alpha is the coefficient of linear thermal expansion in per degree Celsius or per kelvin, L0 is the original length, and delta T is the change in temperature. For small temperature changes this gives an accurate result; for large changes a second-order correction can apply but is usually negligible for engineering work.

What is the difference between linear and volumetric thermal expansion?

Linear thermal expansion describes the change in one dimension (length) of a solid and uses the linear expansion coefficient alpha. Volumetric thermal expansion describes the change in volume and uses the volumetric coefficient beta, which is approximately three times alpha for isotropic solids. Liquids and gases are usually described by their volumetric coefficient only, since they do not have a fixed shape.

Why does thermal expansion matter in engineering?

Structures and components that operate across a range of temperatures must account for expansion and contraction. Bridges include expansion joints to prevent buckling in summer heat. Pipelines use expansion loops or bellows to absorb movement. Railways historically used small gaps between rails. Ignoring thermal expansion can cause cracking, buckling, seal failure, or misalignment in precision machinery.