Thermal Expansion Calculator
Find how much steel, copper, PEX, PVC, aluminium, concrete or glass grows with temperature, the volume change of liquids, and the stress if it is restrained.
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About this toolWhat is the Thermal Expansion Calculator?
Almost every material gets longer when it warms up, and the amount is predictable: change in length equals the coefficient of linear expansion times the original length times the temperature change. A 30 m run of carbon steel pipe heated from 10 °C to 70 °C grows by 21.6 mm. The same run in PEX would grow by almost 300 mm, which is why plastic hot-water lines need loops and offsets that steel lines can do without.
This calculator gives the change in length in millimetres and inches, the final length, the strain, and the stress a perfectly restrained member would develop, σ = E·α·ΔT. It also does volume: solids use the exact cube of (1 + αΔT), liquids use their own volumetric coefficient, and water is handled from its real density curve because its expansion is strongly non-linear. A comparison table shows the same length and temperature change across fifteen common materials.
- Linear expansion, exact solid volume change and liquid volume change
- Fifteen materials with typical α and elastic modulus, all editable
- Exact water expansion from the Kell density equation, 0 to 100 °C
- Restrained stress σ = E·α·ΔT with a yield warning
- Comparison table across materials for the same length and ΔT
How to use the Thermal Expansion Calculator
- Choose length, solid volume or liquid volume, and °C or °F. Switching the temperature unit converts the temperatures and α.
- Pick a material to load its typical α and elastic modulus, or type your own values from a datasheet.
- Enter the original length or volume with its unit, and the start and end temperatures. A negative change means contraction.
- Read the change in length or volume. For lengths, the restrained stress tells you what happens if the ends are fixed.
- Use the comparison table to see how other materials would behave over the same length and temperature change.
Worked examples
Steel pipe run (page default)
Input
Carbon steel, α 12 x 10⁻⁶ /K, 30 m, 10 °C to 70 °C, E 200 GPa
Output
ΔL 21.6 mm (0.850 in), strain 720 µε, restrained stress 144 MPa
Fully anchored at both ends, this pipe would carry 144 MPa of compression, enough to buckle a long unsupported span, which is why anchors and guides are paired with loops.
PEX hot water line
Input
PEX, 50 ft, a 70 °F rise
Output
ΔL 3.85 in
That is the manufacturer rule of about 1.1 in per 100 ft per 10 °F, scaled to half the length and seven times the temperature step.
Hot water tank expansion
Input
Water, 100 L, 10 °C to 60 °C
Output
ΔV 1.68 L
A constant β of 2.07 x 10⁻⁴ would predict only 1.04 L. The extra comes from water expanding faster at higher temperatures, and it is what an expansion vessel must absorb.
Background and insight
The coefficient of linear expansion α is the fractional change in length per kelvin. For metals it is nearly constant over the range of everyday engineering, so ΔL = αLΔT is accurate. Typical values used here: carbon steel 12, stainless 304 17.3, aluminium 6061 23.6, copper 17, concrete about 10 and soda-lime glass about 9, all in millionths per kelvin. Plastics are an order of magnitude higher: PVC around 54, CPVC 61, HDPE 120 and PEX about 165 x 10⁻⁶ /K, which matches the manufacturer rule of roughly 1.1 in per 100 ft per 10 °F.
For an isotropic solid the volume coefficient is three times the linear one, because each of the three dimensions grows by the same fraction. The calculator uses the exact form V[(1 + αΔT)³ − 1], which differs from the 3α shortcut only in the fourth significant figure for normal temperature changes. Liquids have no shape to keep, so they are characterised directly by a volumetric coefficient β. Water is the awkward one: it contracts from 0 to 4 °C, then expands faster and faster, so β at 20 °C (2.07 x 10⁻⁴ /K) underestimates expansion at hot-water temperatures. The calculator uses the Kell (1975) density equation for water instead.
If a member cannot move at all, the strain it would have had becomes a stress. With E = 200 GPa and α = 12 x 10⁻⁶ /K, steel gains 2.4 MPa per kelvin, independent of length. A 60 K rise produces 144 MPa, more than half the yield strength of mild steel. That is the reason pipelines have expansion loops and bridges have expansion joints.
Common use cases
Pipe expansion loops
Get the movement a loop, offset or bellows must take up on copper, steel, PVC or PEX runs between anchors.
Expansion gaps in structures
Size gaps for aluminium curtain wall mullions, steel rails, concrete slabs or glass panels over the service temperature range.
Shrink and press fits
Work out how far to heat a hub or cool a shaft so it slides on, using the diametral change ΔD = αDΔT.
Tank and vessel filling
Estimate how much a fuel or water volume grows on a hot day so tanks are not filled to the brim.
Tips and limitations
- α rises slowly with temperature for metals. For ranges beyond a few hundred kelvin, use a mean coefficient for that range from the material standard.
- Mixed materials move differently. Copper pipe in steel brackets or aluminium in a steel frame needs slotted holes or sliding supports.
- Plastic pipes are also much less stiff, so they develop low stress but large movement and can snake between supports when hot.
- The restrained stress assumes the supports do not move at all. Real anchors flex, which lowers stress but raises anchor loads.
- For diameters, the same formula applies: a 100 mm steel hole grows 1.2 µm per kelvin.
Frequently asked questions
What is the formula for linear thermal expansion?
ΔL = α x L x ΔT, where α is the coefficient of linear expansion per kelvin (or per °F), L is the original length and ΔT the temperature change. The result has the same unit as L.
How much does steel expand per degree?
Carbon steel expands about 12 millionths of its length per kelvin, or 6.7 millionths per °F. That is 0.012 mm per metre per °C, or about 0.8 in per 100 ft for a 100 °F rise.
How much does copper pipe expand?
About 1.1 to 1.2 in per 100 ft for a 100 °F rise, using α of about 17 x 10⁻⁶ /K (9.4 x 10⁻⁶ /°F).
Why is volumetric expansion three times linear expansion?
Each of the three dimensions of an isotropic solid grows by αΔT, so volume grows by (1 + αΔT)³, which is very close to 1 + 3αΔT when αΔT is small.
What stress does thermal expansion cause if a member is fixed?
σ = E x α x ΔT. For steel that is about 2.4 MPa (350 psi) per °C of temperature change, regardless of the member length.
Does water expand uniformly when heated?
No. Water is densest at about 4 °C, contracts slightly when warmed from 0 to 4 °C, and then expands at an increasing rate. From 4 °C to 100 °C its volume grows by about 4.3%.
Which plastic pipe expands the most?
Of the common plumbing plastics, PEX moves the most at about 165 x 10⁻⁶ /K, followed by HDPE around 120, CPVC about 61 and PVC about 54. All are several times more than copper.
Is there an in-depth guide to the Thermal Expansion Calculator?
Yes. “Thermal Expansion in Pipes and Structures: ΔL = αLΔT in Practice” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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