Thermal Expansion Calculator
By Santaji GadepatilinUpdated October 27, 2026
Most materials grow when heated and shrink when cooled. Pipes, rails, bridges and machine parts must allow for this movement, or the stresses can bend, crack or break them. This free thermal expansion calculator solves for whichever value you leave blank and shows the formula and steps.
Change in length (mm) vs Temperature change (K / °C) — other inputs held at your current values.
How to use the thermal expansion calculator
Choose the material, then enter the length and temperature change. The expansion is shown in mm or inches. A negative temperature change gives contraction.
Thermal expansion formula
ΔL = α × L × ΔT
Worked example
A 50 m carbon steel steam line heated from 20 °C to 80 °C (ΔT = 60 K):
ΔL = 12 × 10⁻⁶ × 50 × 60 = 0.036 m = 36 mm
The same run in HDPE would grow about 600 mm — plastic pipes need much more allowance.
Expansion per 10 m for a 50 K rise
| Material | Expansion |
|---|---|
| Carbon steel | 6.0 mm |
| Stainless steel | 8.7 mm |
| Copper | 8.3 mm |
| Aluminium | 11.6 mm |
| PVC | 26 mm |
| HDPE | 100 mm |
Coefficients of linear expansion
| Material | α (×10⁻⁶ per K) |
|---|---|
| Invar | 1.2 |
| Glass (borosilicate) | 3.3 |
| Concrete | 10–12 |
| Carbon steel | 11–13 |
| Stainless steel 304/316 | 16–17 |
| Copper | 17 |
| Aluminium | 23 |
| PVC | 50–80 |
| HDPE | 120–200 |
Plastic pipes expand about 10 times more than steel for the same temperature change.
Volume expansion of liquids
Liquids expand in volume: ΔV = β × V × ΔT. Water’s β is about 0.00021 per K at 20 °C, rising to about 0.0006 near 80 °C. A 1,000 L closed heating system warmed from 10 °C to 80 °C expands by roughly 25–30 L, which is why an expansion vessel is needed.
Thermal stress
If expansion is prevented, stress builds up:
σ = E × α × ΔT
For steel (E = 200 GPa, α = 12 × 10⁻⁶), a 50 K rise in a fully restrained pipe creates 120 MPa of stress — a large share of the yield strength of common steels.
Bimetal strips
Two metals with different α bonded together bend when heated. Thermostats, circuit breakers and dial thermometers use this effect.
Allowing for expansion
Long hot lines need expansion loops, bellows or offsets, and guides and anchors placed to direct the movement. Restraining expansion completely creates very large forces that can damage supports, flanges and connected equipment.
Frequently asked questions
What is the linear expansion formula?
ΔL = α × L × ΔT, where α is the material's coefficient of linear expansion, L the original length and ΔT the temperature change.
How much does steel pipe expand?
Carbon steel grows about 1.2 mm per metre for every 100 °C rise. A 50 m line heated by 60 °C grows about 36 mm.
Is a 1 °C change the same as 1 K?
Yes, for temperature differences. A 1 °F difference equals 5/9 K.
How much does a 100 m steel pipe expand for 50 °C?
12 × 10⁻⁶ × 100 × 50 = 0.06 m, or 60 mm.
Why do bridges have expansion joints?
To allow the deck to lengthen and shorten with temperature without building up damaging stress.