Thermal Expansion Calculator
Enter the expansion coefficient from the grade datasheet, the length at the starting temperature and the temperature change. The engine returns the change in length in millimetres — positive for heating, negative for cooling.
Thermal expansion of a length
Take α from the grade's datasheet for the temperature range in question — it is a mean value over that range, and it rises with temperature. A negative temperature change gives a contraction.
What this calculates
Every metal grows when it is heated and shrinks when it cools, by an amount proportional to its length and to the temperature change. The constant of proportionality is the linear thermal expansion coefficient, written α and given in micrometres per metre per degree Celsius. A three-metre stainless steel rail that warms by fifty degrees grows by a couple of millimetres; over a forty-metre facade run the same warming adds up to tens of millimetres, which is why cladding rails, handrails and pipe runs carry expansion joints and slotted fixings.
The coefficient depends on the alloy, and the differences matter. Austenitic stainless steels sit around 16 to 17 µm/m·°C, ferritic and martensitic grades and carbon steels around 10 to 12, aluminium alloys around 23, and duplex grades in between. Aluminium fixed to steel, or austenitic stainless welded to carbon steel, moves at different rates and the joint sees the difference as stress. This page takes α as you type it, so it works for any grade whose datasheet you have open.
Use the result to size the gap at an expansion joint, to check whether a rigidly fixed length will be pushed into buckling or pulled into tension, and to judge how a long run will move between the coldest night and the hottest afternoon on site. Saudi conditions make this a daily question: a black-painted surface in direct sun reaches well past sixty degrees, and the same member drops toward ten degrees on a winter night.
Show the formula and a worked example
The formula
- ΔL = α × L₀ × ΔT ÷ 10⁶ (α in µm/m·°C, L₀ in mm, ΔT in °C → ΔL in mm)
Dimensions in millimetres, density ρ in kg/m³ — as the engine runs them.
ΔL = α × L₀ × ΔT ÷ 10⁶. The coefficient α is in µm/m·°C, the original length L₀ in millimetres and the temperature change ΔT in °C; dividing by a million converts micrometres per metre into millimetres per millimetre, so the result comes out in millimetres.
ΔT is a difference, so it is the same in °C and in kelvin, and it may be negative. Only α and L₀ must be greater than zero. The coefficient is a mean value over a temperature range; datasheets quote it for 20–100 °C, 20–300 °C and so on, and the higher range gives a slightly larger figure. Pick the range that brackets your service temperatures.
Worked example
| Calculation | Thermal expansion of a length |
|---|---|
| Expansion coefficient α | 17.2 µm/m·°C |
| Original length | 3000 mm |
| Temperature change | 50 °C |
| Theoretical result | 2.58 mm |
Computed by the calculation engine from these inputs at render time, rounded only for display.
Frequently asked
- 01Where do I find α for my grade?
- On the mill or standard datasheet under physical properties, usually as "mean coefficient of thermal expansion" for one or more temperature ranges. Our material pages will carry it once the physical property rows are approved; until then, type the datasheet value in.
- 02Does a negative temperature change work?
- Yes. Enter the drop as a negative number and the result is negative: the length shrinks. The field for temperature change is the only one on the site that accepts a minus sign.
- 03Is the expansion the same in every direction?
- For a flat product or a bar, yes: the same coefficient applies to length, width and thickness, and the volume grows by roughly three times the linear figure. The length dominates in practice because it is the longest dimension.
- 04How do I size an expansion gap from this?
- Compute ΔL for the hottest and the coldest expected temperature relative to the installation temperature, add the two movements, and leave a gap at least that wide plus the installation tolerance. The fixing detail and the sealant then have to accommodate that travel.