Thermal Expansion Calculator

This calculator works out how much a material expands or contracts when its temperature changes, using the linear thermal expansion formula. Almost all materials grow slightly when heated and shrink when cooled, because rising temperature makes their atoms vibrate more and push a little further apart. The amount is tiny for a small object but becomes significant over long lengths and large temperature swings, which is why engineers must account for it: bridges and railway lines have expansion joints, pipes and power lines are installed with slack, and precision instruments are designed to minimise it. The expansion depends on three things: the original length, the temperature change, and the material's coefficient of linear expansion, a number that captures how much that particular material stretches per degree. This tool computes it. You enter the original length, the coefficient of linear expansion, and the temperature change, positive for heating or negative for cooling, and the calculator returns the change in length, the new length, and the strain, the fractional change. The results update as you type, so you can see how a longer span or a bigger temperature swing increases the movement. Use it for engineering and construction, for understanding expansion joints and tolerances, or for physics study. The formula is simply the change in length equals the coefficient times the original length times the temperature change. A practical insight it makes clear is the role of length: because expansion is proportional to the original length, a long steel bridge or rail can move by centimetres across the seasons even though the coefficient is small, which is exactly why expansion gaps are essential. Different materials expand at very different rates, so the coefficient is the key figure to get right for your material.

3.6 mm
change in length
New length10.0036 m
In metres0.0036 m
Strain0.00036

Linear expansion: change in length = coefficient x original length x temperature change. Use scientific notation for the coefficient (steel ~12e-6, aluminium ~23e-6 per °C).

How it works

The change in length is the coefficient of linear expansion multiplied by the original length and the temperature change. Adding this to the original length gives the new length. The strain, the fractional change in length, is simply the coefficient times the temperature change, independent of the length.

Worked example

A 10 metre steel beam with an expansion coefficient of 12 times 10 to the minus 6 per degree, warmed by 30 degrees, expands by 12 times 10 to the minus 6, times 10, times 30, which is 0.0036 metres, or 3.6 millimetres. Its new length is 10.0036 metres, a small but real movement that matters over long spans.

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