What this calculator does
Almost everything expands when heated. The amount is small in percentage terms but very significant over long spans, which is why bridges have expansion joints, rails have gaps and long pipe runs include loops.
The change depends on three things multiplied together: the original length, the temperature change and the material's coefficient of expansion. Because the original length is a factor, the same temperature swing moves a long span far more than a short one.
The formula
Multiply the coefficient of linear expansion by the original length and by the temperature change. The result is the change in length in the same units as the original length.
| Term | Meaning |
|---|---|
| Coefficient of linear expansion (α) | The fractional change in length per degree of temperature change. Steel is about 12 millionths per degree celsius. |
| Strain | The change in length divided by the original length, a dimensionless measure of how much the material has stretched. |
| Expansion joint | A deliberate gap or flexible section that absorbs thermal movement so it does not become stress. |
The inputs explained
| Field | What to enter |
|---|---|
| Original length (m) | The original length at the starting temperature, in metres. |
| Coefficient of linear expansion (steel ≈ 12×10⁻⁶) (1/°C) | The coefficient of linear expansion for the material, per degree celsius. Steel is about 0.000012; aluminium roughly double that; concrete similar to steel, which is why they work together. |
| Temperature change (°C) | The temperature change in degrees. Use a negative value for cooling. |
When to use it
Sizing an expansion gap
A run of pipe or rail that will see a known temperature range needs a gap at least as large as the movement it will experience.
Understanding a stuck fitting
Heating a metal collar expands it slightly, which is often enough to free a part that is otherwise seized.
Checking a precision measurement
Measurements taken at different temperatures differ slightly, which matters for machining and for long survey baselines.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does 10 m of steel move with temperature?
A ten metre steel span across a range of temperature changes.
| Temperature change | Change in length | Strain (ΔL/L₀) |
|---|---|---|
| 20°C | 0.002400 m | 0.000240 |
| 40°C | 0.004800 m | 0.000480 |
| 60°C | 0.007200 m | 0.000720 |
| 80°C | 0.009600 m | 0.000960 |
Questions
Why do bridges need expansion joints?
Because a long span moves substantially over a year of temperature change, and a structure held rigidly would develop enormous internal stress instead. The joint lets the movement happen harmlessly.
What happens if expansion is prevented?
The movement becomes stress instead. Thermal stress can easily exceed what a member was designed for, which is how rails buckle in extreme heat when the gaps close up completely.
Why can concrete and steel be used together?
Because their expansion coefficients are remarkably similar. Reinforced concrete works partly because the steel and the concrete expand at close to the same rate, so temperature changes do not tear them apart.
Does this apply to area and volume too?
Yes, with different coefficients. Area expansion is approximately twice the linear coefficient and volume expansion approximately three times, because the linear change applies in each dimension.
For the heat energy behind the temperature change, see the specific heat calculator. For the stress that results when expansion is restrained, see the mechanical stress calculator.