How to use it
- Choose the Material of the part, for example Aluminium.
- Type the Length, m and the Volume, L of the part before the change, for example 10 and 1.
- Type the Change in temperature, °C, for example 50 for a rise of 50 degrees.
- Read the Change in length, mm and the Change in volume, mL, then the steps.
How the expansion is calculated
A solid grows when it is heated, because its atoms vibrate more widely and push each other apart. For a change in temperature that is small compared with the temperature itself, the change in length and in volume are proportional to the change in temperature (OpenStax, University Physics Volume 2, Section 1.3).
ΔL = α × L × ΔT
ΔV = β × V × ΔT
ΔL = change in length, m
ΔV = change in volume, in the unit of V
α = linear coefficient, per °C
β = volume coefficient, per °C
L = length before the change, m
V = volume before the change
ΔT = change in temperature, °C- The change is proportional to the length: twice the length gives twice the change.
- Each material has its own coefficient. Over the same change in temperature, invar changes about 28 times less in length than aluminium.
- A fall in temperature gives a negative change, so the part shrinks.
The coefficients used
The values are those of Table 1.2 of the OpenStax section, for solids, in units of 10⁻⁶ per degree Celsius. The section does not state the reference temperature of its table.
| Material | α, 10⁻⁶ /°C | β, 10⁻⁶ /°C |
|---|---|---|
| Aluminium | 25 | 75 |
| Brass | 19 | 56 |
| Copper | 17 | 51 |
| Gold | 14 | 42 |
| Iron or steel | 12 | 35 |
| Invar (nickel-iron alloy) | 0.9 | 2.7 |
| Lead | 29 | 87 |
| Silver | 18 | 54 |
| Ordinary glass | 9 | 27 |
| Pyrex glass | 3 | 9 |
| Quartz | 0.4 | 1 |
| Concrete or brick | 12 | 36 |
| Marble | 2.5 | 7.5 |
What the calculator does not include
- Liquids and gases. The source gives them only by a volume coefficient; water's is 210 × 10⁻⁶ per °C in the same table.
- Large changes of temperature, where the coefficient itself changes with the temperature.
- Stress in a part that is held so that it cannot expand. That needs the stiffness of the material and the design of the joint.
Worked example: 10 m of aluminium heated by 50 °C
The change in length is ΔL = 25 × 10⁻⁶ /°C × 10 m × 50 °C = 0.0125 m, which is 12.5 mm, so the new length is 10.0125 m. For 1 L of the same metal the change in volume is ΔV = 75 × 10⁻⁶ /°C × 1 L × 50 °C = 0.00375 L, which is 3.75 mL.
| Figure | Value |
|---|---|
| Change in length | 12.500 mm |
| New length | 10.0125 m |
| Change in volume | 3.750 mL |
Frequently asked questions
Why does a metal rod get longer when it is heated?
Heating makes the atoms vibrate more widely, so on average they sit farther apart. The change is small for each degree, but it adds up over the length of the rod.
Is the volume coefficient always three times the linear one?
In the OpenStax table the volume values equal three times the linear ones except for rounding. The calculator uses the printed values as they are, so the result follows the table.
Can the calculator give the expansion of water?
Not as a material. Water appears in the source only with a volume coefficient, and the calculator covers solids. For water, multiply the volume by 210 × 10⁻⁶ per degree and the change in temperature by hand.
How big a change in temperature is small enough?
The source calls a constant coefficient quite accurate for small changes of temperature and gives no fixed limit. For large changes, or a precise design, use a coefficient measured at the working temperature.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you type is sent to us or stored.
Sources
Figures and text last checked on Wednesday, November 11, 2026.