Work out how much a part, pipe, rail or tank of liquid grows or shrinks when its temperature changes. Pick a material (metals, plastics, glass, concrete or liquids) or enter your own coefficient, choose linear, area or volume expansion, and get the new size, the percentage change and the stress if the part is held fixed.
Last updated:
Type of expansion
Material
GPa
Only for the restrained-stress estimate
Size
Temperature
Temperature input
Negative for cooling
Enter your values to see the result.
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How to use the Thermal Expansion Calculator
Choose the type: linear for rods, pipes and rails; area for plates; volume for solids or liquids.
Pick the material from the list, or choose Custom and type a coefficient from a datasheet.
Enter the starting size and its unit.
Enter the temperatures (start and end) or just the change ΔT, in °C, °F or K.
Read the change and final size, then compare materials in the table below the results.
Thermal expansion formulas
Linear: ΔL = α × L₀ × ΔT, new length L = L₀ (1 + αΔT)
Area: ΔA ≈ 2α × A₀ × ΔT (exact for a plate: A₀(1 + αΔT)²)
Volume: ΔV = β × V₀ × ΔT, with β ≈ 3α for solids (exact cube rule V₀(1 + αΔT)³)
Restrained stress: σ = E × α × ΔT, where E is Young’s modulus
Units: α per °F × 1.8 = α per °C; ΔT in °F × 5/9 = ΔT in °C
The linear formulas are first-order approximations. They are very accurate for metals and ceramics over everyday temperature ranges, because αΔT is tiny (a few parts per thousand). For plastics or very large temperature swings the coefficient itself changes with temperature, so treat the result as an estimate.
Typical coefficients of linear expansion
Material
α (×10⁻⁶ /°C)
α (×10⁻⁶ /°F)
Growth per 100 ft for +50 °F
Invar
1.2
0.67
0.04 in
Borosilicate glass
3.3
1.8
0.11 in
Cast iron
10.8
6.0
0.36 in
Carbon steel / concrete
12
6.7
0.40 in
Copper
16.5
9.2
0.55 in
Stainless steel 304
17.3
9.6
0.58 in
Brass
19
10.6
0.63 in
Aluminum
23.1
12.8
0.77 in
PVC (rigid)
52
29
1.73 in
ABS
99
55
3.3 in
HDPE
≈150
≈83
≈5.0 in
The values are typical for room temperature. Grades and blends differ, so check the product datasheet for critical work.
Practical tips
Use the full temperature range the part will see, from installation temperature to the hottest and coldest service conditions. For outdoor pipe or siding that can be more than 100 °F.
Plastics move a lot. PVC, ABS and PE grow 4 to 12 times more than steel, so long runs need expansion loops, offsets or sliding supports.
Mixed materials (an aluminum part bolted to steel, a glass pane in a metal frame) build stress or open gaps because they grow at different rates. Compare them in the table.
Liquids in closed containers such as water heaters and fuel tanks expand much more than the container, which is why they have expansion tanks, relief valves or headspace.
Frequently asked questions
What is the formula for linear thermal expansion?
ΔL = α × L₀ × ΔT, where α is the linear expansion coefficient (per °C), L₀ the original length and ΔT the temperature change. A 100 ft carbon-steel member (α ≈ 12 × 10⁻⁶ /°C) warmed by 70 °F (38.9 °C) grows about 100 × 12e-6 × 38.9 = 0.047 ft, roughly 0.56 inch.
How is volumetric expansion related to linear expansion?
For an isotropic solid the volumetric coefficient is about three times the linear one (β ≈ 3α) and the area coefficient about twice (2α). Liquids have no fixed shape, so they are described only by β, measured directly.
How do I convert a coefficient from per °F to per °C?
A temperature change of 1 °F is 5/9 of 1 °C, so a coefficient per °C is 1.8 times the same coefficient per °F. For example 6.5 × 10⁻⁶ /°F equals 11.7 × 10⁻⁶ /°C. A change of 1 K is identical to a change of 1 °C.
How much does copper or PVC pipe expand?
Copper (α ≈ 16.5 × 10⁻⁶ /°C) grows about 1.1 inch per 100 ft for a 50 °F rise. Rigid PVC (about 52 × 10⁻⁶ /°C) grows over three times as much, roughly 3.5 inches per 100 ft for the same rise, which is why long plastic runs need expansion loops or offsets.
What happens if a part cannot expand?
It builds internal stress instead. For a bar held between rigid supports the stress is σ = E × α × ΔT. Heating a fully restrained steel bar by 40 °C gives about 200 GPa × 12e-6 × 40 ≈ 96 MPa (14,000 psi) of compression, enough to buckle slender members, which is why bridges, rails and pipelines use expansion joints.
Are the coefficients exact?
No. Coefficients vary with alloy, grade, moisture and temperature range, and plastics vary widely. The presets are typical room-temperature values; for design work use the manufacturer’s datasheet value with the Custom option. The linear formula also assumes the coefficient stays constant over your temperature range.
Why does water behave differently?
Water is unusual: its expansion coefficient rises with temperature (about 207 × 10⁻⁶ /°C at 20 °C, much more near boiling) and it actually contracts when warmed from 0 to 4 °C. The water preset uses the 20 °C value, so results for large temperature swings are approximate.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.