Thermal Expansion Calculator
When a solid is heated or cooled, it changes in length and volume according to its thermal expansion coefficient. Linear thermal expansion describes how the length of an object changes: delta-L = alpha times L0 times delta-T, where alpha is the linear coefficient of thermal expansion measured in per degree Celsius (or per kelvin, which is the same interval), L0 is the original length, and delta-T is the temperature change. Volumetric thermal expansion describes how volume changes: delta-V = beta times V0 times delta-T, where beta is approximately three times alpha for isotropic materials. This calculator accepts original length or volume, the material (with pre-filled alpha values for steel, aluminum, concrete, glass, copper, and wood), and temperature change. Results show the expansion amount and the new total dimension. Understanding thermal expansion is essential in civil engineering, mechanical design, electronics, and precision manufacturing. All coefficient values shown are standard reference figures.
Length change: -- m | New length: -- m
Thermal expansion formulas
Linear: delta-L = alpha * L0 * delta-T
New length: L = L0 * (1 + alpha * delta-T)
Volumetric: delta-V = beta * V0 * delta-T (beta = 3 * alpha)
New volume: V = V0 * (1 + beta * delta-T)
Worked example
- Steel rail, original length 10 m, temperature rise of 40 °C
- Alpha for steel = 12 * 10^-6 per °C
- delta-L = 12e-6 * 10 * 40 = 0.0048 m = 4.8 mm
- New length = 10.0048 m
Linear thermal expansion coefficients
| Material | Alpha (per °C) |
|---|---|
| Invar (Fe-Ni alloy) | 3 x 10^-6 |
| Glass (borosilicate) | 3.3 x 10^-6 |
| Glass (ordinary) | 9 x 10^-6 |
| Concrete | 12 x 10^-6 |
| Steel | 12 x 10^-6 |
| Iron | 12 x 10^-6 |
| Copper | 17 x 10^-6 |
| Aluminum | 24 x 10^-6 |
Frequently asked questions
What is thermal expansion?
Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. When a material absorbs heat, its particles vibrate more vigorously and push further apart, causing the material to expand. Most solids, liquids, and gases expand when heated. The amount of expansion depends on the material (its thermal expansion coefficient), the original size, and the temperature change.
What is the linear thermal expansion formula?
The linear thermal expansion formula is delta-L = alpha * L0 * delta-T, where delta-L is the change in length, alpha is the linear coefficient of thermal expansion (per °C or per K), L0 is the original length, and delta-T is the temperature change. The new length is L = L0 + delta-L = L0 * (1 + alpha * delta-T).
How does volumetric expansion relate to linear expansion?
For isotropic materials (materials that expand equally in all directions), the volumetric (cubic) coefficient of thermal expansion beta is approximately equal to three times the linear coefficient: beta = 3 * alpha. This is because volume is a three-dimensional quantity. So delta-V = beta * V0 * delta-T, and the new volume is V = V0 * (1 + beta * delta-T).
Why do engineers account for thermal expansion?
Thermal expansion can cause structural stress if materials are constrained from expanding freely. Examples include: expansion joints in bridges and railway tracks (to prevent buckling in summer heat), gaps left between concrete panels in sidewalks and roads, allowances in piping systems carrying hot fluids, and design of precision instruments and machinery. Failure to account for thermal expansion can lead to cracks, warping, joint failure, or catastrophic structural damage.
Why does concrete have a similar expansion coefficient to steel?
Reinforced concrete is so practical partly because concrete and steel have very similar linear thermal expansion coefficients (both around 12 times 10 to the power of negative 6 per °C). If they expanded at different rates, temperature changes would cause the steel reinforcing bars to pull away from or crush the surrounding concrete, destroying the composite structure. This fortunate compatibility is one reason reinforced concrete has been so widely used in construction since the 19th century.
Sources
- Engineering ToolBox: Linear Expansion Coefficients.
- NIST: Materials Measurement Laboratory.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.