Free · Calculator 7
Thermal expansion and expansion compensation
Change in length between anchor points from installation, minimum and maximum temperature, compensator with pre-tension and a first estimate for L-, Z- and U-bends.
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Basis & sources
What the tool calculates with, which standards and data it relies on and where its limits are. As of September 2026. For practice: Understand it and try it out.
Calculation method
- ExpansionΔL = α·L·ΔT with mean coefficient of thermal expansion from 20 °C
- CompensatorTotal movement + 10%, cold spring to mid-position
- Expansion legguided cantilever: L = √(3·E·D·δ / σ)
- NextPlan support spans and supports
Standards & codes
Reference: the assistant follows Autodesk's file structure and the connection types of these standards. Standard texts and standard tables are not included.
| DIN EN 13480-3, ASME B31.3 | Stress verification in the pipe stress analysis (not part of the calculator) |
|---|---|
| DIN EN 13445-3, Annex O | Modulus of elasticity over temperature as in the Support Span Calculator |
Data & origin
| Coefficients of thermal expansion α | Guide values per material group with range of validity – table in the calculator ("where does α come from?") |
|---|---|
| Allowable bending stress | Guide value, editable in the calculator |
Assumptions & limits
- Estimate of whether a bend fits – not a pipe stress analysis (anchor forces, support friction, stress verification).
- Values outside the range of validity of α are flagged ("Not usable as is").
- Plastic: expansion about 10 to 15 times that of steel, modulus of elasticity time-dependent – observe the manufacturer data.
Standards status for this page 2 standards · researched September 2026
| Standard | Contents | Current edition | Replaced / successor |
|---|---|---|---|
| DIN EN 13480-3 | Metallic industrial piping – Part 3: Design and calculation | DIN EN 13480-3:2024-12 | replaces DIN EN 13480-3:2017-12; DIN EN 13480-3/A1:2021-05; DIN EN 13480-3/A2:2020-12 |
| ASME B31.3 | Process Piping | ASME B31.3-2024 | replaces ASME B31.3-2022 |
Researched at DIN Media, ISO, IEC and ASME, as of September 2026. Before binding use, please check the current edition with the standards publisher. Overview of all standards: Plant Engineering Infobase · Standards status.
Understand it and try it out
Metal and plastic get longer when they heat up. A few millimeters per meter sounds harmless – over a 40 m line it quickly adds up to 8 cm, and that has to go somewhere. Here you can see how much it is and how to absorb it.
The terms in five minutes
- Coefficient of thermal expansion α
- How much longer a material gets per kelvin, e.g. steel around 12 · 10⁻⁶/K: 1 m gets 1.2 mm longer when heated by 100 K. Plastics expand 10 to 15 times as much.
- Change in length ΔL
- ΔL = α · L · ΔT. Double the length or double the temperature difference → double the expansion.
- Anchor point
- Holds the line in place at one point. Between two anchor points, the expansion must be absorbed.
- Sliding and guide supports
- Carry the pipe but let it move longitudinally (sliding support) or only in one direction (guide).
- Compensator
- A bellows that absorbs the movement. Axial compensators absorb longitudinal movement but need anchor points that take up the internal pressure.
- Expansion leg / U-loop
- A transverse pipe section that bends elastically – the "natural" compensation without bellows. Needs space.
- Pre-tension
- The compensator is installed slightly stretched or compressed at installation temperature so that it works around its mid-position in operation.
Try it out and understand it
Change one value in the calculator above and watch what happens to the others:
| Try it | What happens | Why |
|---|---|---|
| Change the material from steel to PE 100 (same temperatures) | The expansion becomes about 15 times as large. | α of PE is about 180 · 10⁻⁶/K versus 12 · 10⁻⁶/K for steel. Plastic lines need much more expansion compensation – even with a small temperature range. |
| Set the installation temperature from 10 to 30 °C | Expansion in operation decreases, contraction in winter increases – the pre-tension may change direction. | What matters is the difference from the installation temperature, not the absolute temperature. |
| Double the pipe outside diameter | The required expansion leg becomes about 1.4 times as long. | L ~ √D: thicker pipes are stiffer and need longer legs to absorb the same displacement without excessive stress. |
| Enter PVDF at 600 °C | The calculator calculates but shows red: "Not usable as is". | You can calculate anything – whether the material can withstand it is another question. Always check the operating range. |
Typical mistakes
- Considering only Tmax and forgetting the contraction at standstill – it pulls on nozzles and anchor points.
- Installing the compensator without pre-tension – it then runs against its stop in operation.
- Forgetting anchor forces: an axial compensator transfers the internal pressure as a force to the anchor points.
- Treating plastic like steel: with plastics, the modulus of elasticity and allowable stress depend strongly on temperature and time.
For practice
Exercise: A 40 m steel line is installed at 10 °C and heated to 180 °C in operation. How much longer does it get? And roughly how long would an L-shaped expansion leg need to be for a 114.3 mm pipe?
Show solution
α (20 → 180 °C) ≈ 12.5 · 10⁻⁶/K; ΔL = 12.5·10⁻⁶ · 40,000 mm · 170 K ≈ 85 mm – so around 8 to 9 cm. Expansion leg per L = √(3 · E · D · δ / σ) with E ≈ 190,000 N/mm² (hot), D = 114.3 mm, δ = 85 mm, σ = 120 N/mm²: L ≈ √(3 · 190,000 · 114.3 · 85 / 120) ≈ 6.8 m. That is a lot of space – which is why long lines are divided by anchor points or fitted with U-loops or compensators. In the calculator: material steel, 40 m, 10 / −10 / 180 °C, outside diameter 114.3.
For training and studies: this page may be shown in class. Property values are guide values; for verification, the standards and manufacturer data apply.
What is the calculator for?
Why you need it
Pipelines get longer when heated – 40 m of steel pipe at 180 °C by around 8 cm. If the line cannot move freely, it pushes with large forces on anchor points and on the nozzles of pumps, vessels and heat exchangers: flanges leak, supports tear out, nozzles deform.
Which tasks it solves
- How far does the line move between two anchor points?
- Is the routing with its bends sufficient – or is a U-loop or compensator needed?
- What movement capacity does the compensator need, and how far is it pre-tensioned during installation?
- How much clearance do wall penetrations, pipe clamps and insulation need?
When in the design process
- Basics / preliminary design–
- Basic engineeringRouting and layout planning: provide space for bends, U-loops or compensators
- Detail engineeringDefine anchor points and sliding supports, check plausibility before pipe stress analysis
- Installation / commissioningInstall compensators with the correct pre-tension
- Operation / modification of existing plantsModification: can the new routing handle the temperature?
Frequently asked questions
Does this replace a pipe stress analysis?
No. The estimate shows whether a bend realistically fits. Anchor forces, support friction and stress verification per DIN EN 13480-3 or ASME B31.3 belong in the pipe stress analysis.
Why is plastic so critical?
Thermal expansion is about 10 to 15 times that of steel, the modulus of elasticity is low and time-dependent – design expansion legs and support spacing according to manufacturer data.
Preliminary sizing for design work – not a verification. Dimensions and material properties come from the ASEING Piping Spec Calculator and Support Span Calculator and are estimates from publicly available manufacturer data, generalized; all other values are guide values. They may deviate from the standard – check against the applicable standards and manufacturer data before binding use. You can enter your own values in the calculator.