Science & Engineering
Thermal expansion.
How much longer (or shorter) a bar, pipe or span gets when the temperature changes: ΔL = α × L × ΔT. Pick a material or enter your own coefficient. Runs in your browser.
Material, length and temperatures
Result
Fill the form and press Calculate.
Worked example
A 10 m aluminium bar (α = 23 × 10⁻⁶ per °C) warms from −10 °C to 30 °C, a change of 40 °C. ΔL = α × L × ΔT = 0.000023 × 10 m × 40 = 0.0092 m, so it grows by 9.2 mm (0.362 in) to 10.0092 m. A steel bar of the same size, using the middle of its listed range (11.65 × 10⁻⁶ per °C), grows 4.66 mm.
How it works
When a solid is heated or cooled its length changes in proportion to its original length and the temperature change: ΔL = α × L × ΔT, where α is the linear expansion coefficient. The coefficients here are tabulated values in millionths per °C (10⁻⁶ per °C). For materials listed as a range, such as steel (10.8 to 12.5) or PVC (54 to 110), the calculator uses the middle of the range and tells you the spread, because the real figure depends on the alloy, grade and temperature range. Fahrenheit temperatures are converted to a Celsius change before use.
This is free, unrestrained expansion of one dimension. It does not compute the force if a part is restrained, and it assumes the coefficient is constant over the range, which is a good approximation for modest temperature changes. Expansion joints, pipe loops and gaps are design decisions to confirm with a qualified engineer or the product maker.
Not for structural design
Planning and learning aid only. It is not for structural, pressure-system or other safety-critical design, and it is not professional engineering advice. Have a qualified engineer check anything that carries people or could fail dangerously.
Sources and basis: Linear Thermal Expansion: Formula, Coefficients & Calculator (Engineering ToolBox); Linear Thermal Expansion Coefficients of Materials (Engineering ToolBox). Checked 2026-10-08. Planning aid only; see the note above.
FAQ
What is the thermal expansion formula?
ΔL = α × L × ΔT: the change in length equals the expansion coefficient times the original length times the temperature change.
How much does steel expand?
Carbon steel is listed at 10.8 to 12.5 millionths per °C, so a 10 m bar warmed by 40 °C grows roughly 4.3 to 5.0 mm.
How much do plastics expand compared with metals?
Much more. PVC is listed at 54 to 110 and polyethylene at 108 to 200 millionths per °C, against 23 for aluminium and about 12 for steel.
Does it work for cooling?
Yes. A final temperature below the start gives a negative change, which means the part shrinks.
What if the part is held at both ends?
It cannot expand freely and pushes on its supports with a large force. This calculator covers free expansion only; ask an engineer about restrained members.