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Thermal expansion compensation calculator
Results
Linear expansion coefficient: 0.012 [mm/m*K]
Temperature difference ΔT: 70 [°C]
Pipe length L: 10 [m]
Extension ΔL: 8.4 [mm]
Arm length L: 1.01 [m]
Arm length U: - [m]
Arm length (pre-tension) U50%: 0.32 [m]
Arm spacing RU: 0.16 [m]
Pipe thermal expansion and compensation calculator
Professional calculator for computing thermal expansion of installation pipes and sizing L-shaped and U-shaped compensation arms. Calculations are based on the linear thermal expansion formula, using expansion coefficients for seven pipe types: steel (seamless and seamed), copper, PEX, PEX/Al, PP and PP-Al.
Designed for HVAC designers, plumbing engineers and installers. The calculator sizes L and U compensation arms (including 50% pre-stretch variant), and the result can be downloaded as a PDF drawing ready to attach to project documentation.
How to use the calculator in 3 steps
Select the pipe type (steel, copper, PEX, PEX/Al, PP, PP-Al) and the appropriate diameter from the predefined series. The calculator automatically assigns the correct linear expansion coefficient for the selected material.
Enter the pipe section length in metres, the maximum working temperature and the installation temperature. The calculator determines the temperature difference (deltaT) needed to compute the expansion.
Read the results: thermal expansion in mm, L and U compensation arm lengths and arm spacing. The result is presented graphically on a diagram and can be downloaded as a PDF.
What the calculator computes
The calculator determines the following values:
- deltaL — thermal expansion of the pipe [mm], resulting from the difference between working and installation temperatures and the linear expansion coefficient of the material.
- L compensation arm — minimum length of the arm perpendicular to the pipe axis, providing expansion compensation in an L-shape (90-degree elbow).
- U compensation arm — minimum arm length of the U-shaped compensator, more compact than L-type compensation.
- U arm with pre-stretch (U50%) — variant with cold pre-stretch to 50% of the expansion, allowing shorter compensation arms.
- Arm spacing RU — distance between U-compensator arms, essential for correct placement in shafts or pipe channels.
Input data — what to enter and where to find it
Pipe type
Select the pipe material. Each material has a different linear expansion coefficient: steel (0.012 mm/m*K) and copper (0.0165 mm/m*K) expand relatively little, while plastics expand much more — PEX at 0.18 mm/m*K (15 times more than steel). Multilayer pipes PEX/Al (0.026 mm/m*K) and PP-Al (0.03 mm/m*K) have intermediate values thanks to the aluminium insert.
Pipe diameter [mm]
External pipe diameter from the standard series. The diameter affects compensation arm lengths — the larger the diameter, the longer the arms for the same expansion. After selecting the pipe type, available diameters load automatically.
Pipe length [m]
Length of the pipe section between two fixed points (anchors). Thermal expansion is directly proportional to length — a 10 m pipe expands twice as much as a 5 m pipe at the same temperature difference.
Maximum working temperature [C]
Highest fluid temperature during normal operation. For radiator heating typically 70-80 C, underfloor heating 35-45 C, domestic hot water 55-60 C, industrial and steam installations up to 100-150 C.
Installation temperature [C]
Ambient temperature during pipe installation. In shell-stage buildings in winter it can be as low as 5-10 C, in summer 20-30 C. The greater the difference between working and installation temperatures, the larger the expansion and compensation arms.
Thermal expansion formula
The calculator uses the fundamental physics formula for linear thermal expansion of solids:
- deltaL — change in pipe length [mm]
- L — initial pipe length [m]
- deltaT — difference between working and installation temperature [C or K]
- alpha — linear expansion coefficient of the material [mm/(m*K)]
Design tips
Every pipe section between two fixed points (anchors) must have thermal expansion compensation. Fixed points divide the installation into independent compensation sections. Between fixed points, sliding supports are used to allow axial pipe movement. Cold pre-stretch to 50% of the expansion reduces required compensation arms by approx. 30% and equalises stresses — the pipe works in both directions. For plastic pipes (PEX, PP), compensation is particularly important due to their very high expansion coefficient.
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Want to learn the theory and compensation methods?
A complete guide to thermal expansion of pipes — formulas, coefficient tables, compensation methods (L, U, Z, bellows and stuffing-box compensators), pre-stretch, calculation examples and common installation mistakes:
Thermal expansion of pipes — calculations, compensation and online calculator