Engineering Guide · Expansion joints

How to Calculate Thermal Expansion of a Pipeline

Every pipe gets longer when heated and shorter when cooled. We cover the formula, coefficients for different materials and calculate the movement an expansion joint must absorb.

Updated: 23 October 2026Reading time: 6 min✓ Reviewed by a OnePROM engineer
Steel pipeline with a bellows expansion joint on an industrial pipe rack

Calculation formula

Pipeline expansion is directly proportional to its length and the temperature difference. The longer the section and the hotter it gets, the more expansion has to go somewhere.

ΔL = α · L · Δt
  • ΔL — expansion of the section, mm;
  • α — linear expansion coefficient of the material, mm/(m·°C);
  • L — length of the section between anchors, m;
  • Δt — temperature difference, °C: operating temperature minus installation temperature.

Calculate each section between two anchors separately: this is the expansion the joint has to absorb.

Pipeline without an expansion joint buckled upward by thermal expansion
If the expansion has nowhere to go, the pipe buckles upward or cracks at a weld.
ANCHORPOINT ANCHORPOINT BELLOWS EXPANSION JOINT pipe guidespipe guides ΔL/2ΔL/2 L — SECTION LENGTH
A section between two anchors: the expansion ΔL is absorbed by the joint, while guides keep the pipe on its axis.

Expansion coefficients

The coefficient α depends on the pipe material. Below are average values for 20–100 °C used for preliminary calculations.

Materialα, mm/(m·°C)α, 10⁻⁶ 1/°C
Carbon steel (St20, 09G2S)0.01212
Stainless steel (12Kh18N10T, AISI 321)0.016616.6
Copper0.01717
Aluminium0.02424
Polypropylene (PP-R)0.15150
Polyethylene (HDPE)0.2200

Reference values. For high temperatures and precise calculations, use reference data for the specific material grade.

Expansion of a 100 m steel pipeline

A ready-made table for a 100-metre section to quickly estimate the scale.

MaterialΔt = 50 °CΔt = 100 °CΔt = 150 °CΔt = 200 °C
Carbon steel, mm60120180240
Stainless steel, mm83166249332

For a different length, scale proportionally: 50 metres — half as much, 200 metres — twice as much.

Worked example

A carbon steel district heating section 60 m long between anchors. Installed at +10 °C, operating temperature +130 °C. The pipeline runs above ground and can cool down to −40 °C during a winter shutdown.

  1. Expansion when heated: 0.012 × 60 × (130 − 10) = 86.4 mm.
  2. Contraction when cooled: 0.012 × 60 × (10 − (−40)) = 36 mm.
  3. Total joint movement: 86.4 + 36 = 122.4 mm.

The expansion joint for this section must absorb at least 122 mm, with a margin. Note that cold contraction added more than 40% to the movement. In the Arctic, where pipelines are installed in summer and stand at −50 °C in winter, this part must never be skipped.

Online calculator

Expansion when heated—
Contraction when cooled—
Total joint movement—

The result is a preliminary estimate. A OnePROM engineer will select the joint precisely, taking pressure, medium and joint type into account.

Select an expansion joint for this result

How to absorb expansion

Self-compensation

Expansion is absorbed by bends in the route — L- and Z-shaped sections. This is the cheapest option, but it only works if the route allows it and the bend legs are long enough.

U-shaped expansion loops

A loop made of the same pipe. Reliable and maintenance-free, but it takes up a lot of space and adds hydraulic resistance.

U-shaped expansion loop on a heating main
U-shaped expansion loop: the expansion is absorbed by the bending of the loop.

Bellows expansion joints

A corrugated stainless steel bellows absorbs expansion by compressing and extending. Compact and installed in-line — which is why they are chosen for heating networks, process pipelines and tight routes.

Cutaway of a bellows expansion joint: corrugated stainless steel bellows
The bellows is a corrugated stainless steel shell.

We will select a bellows expansion joint for your calculated movement, pressure and medium.

Expansion joints catalogue

Anchors and guides

An expansion joint only works together with supports. Anchors divide the pipeline into sections, and each section gets its own joint. The force from expansion and internal pressure is transferred to the anchors, which are designed for this load.

Guides keep the pipe on its axis so that an axial joint does not bow sideways. According to EJMA recommendations, the first guide is placed no further than 4 pipe diameters from the joint, the second no further than 14 diameters.

Anchor and pipe guides on a pipe rack
The anchor takes the force, the guides keep the pipe on its axis.

FAQ

How much does a steel pipe expand when heated?
Carbon steel expands by about 1.2 mm per metre for every 100 °C of heating. A 100-metre section heated by 100 °C becomes 120 mm longer.
Which temperature should be taken as the starting point?
The temperature at which the section is closed — welded to the anchors. Both expansion when heated to operating temperature and contraction when cooled below installation temperature are calculated from it.
Should pipeline cooling be taken into account?
Yes. If the pipeline can cool below its installation temperature — during a winter shutdown or on an above-ground route — it will contract. The joint is selected for the total movement: expansion plus contraction.
Why does an expansion joint only work between anchors?
Anchors divide the pipeline into sections and set the point from which expansion is measured. Without them, the pipe moves randomly and the load goes to equipment and welds.
How does the calculation differ for stainless steel and polypropylene?
Only in the coefficient α. Stainless steel expands about 1.4 times more than carbon steel, and polypropylene more than 10 times. The formula stays the same.
Which expansion joint to choose based on the result?
If the route allows, use self-compensation at bends. If space is limited, install U-shaped loops or bellows joints. A bellows joint is chosen with a movement capacity no less than the calculated total movement, with a margin.

What to choose

Bellows expansion jointsAxial, lateral and angular — for heating networks and process pipelines. Pipeline fittingsElbows, reducers, tees and flanges to GOST for section installation. Calculation for your projectSend us the route layout — we will calculate the expansion and select the joints.

Read next

Damaged bellows expansion joint on a pipeline, close-up
Expansion joints

Why Bellows Fail: 8 Causes of Expansion Joint Failure

Excessive movement, torsion, supports, corrosion, vibration and installation errors — plus a checklist to avoid them.

Reading time: 7 min
Pump station with variable frequency drive cabinets
Drives

Variable Frequency Drive on a Pump: How Much It Saves

Why power drops with the cube of speed, a worked example and a savings and payback calculator.

Reading time: 6 min
← All guide articles

Need a compensation calculation?

Send us the route layout, temperatures and pressure — we will calculate the expansion and select expansion joints for your project.

Request a calculation