Pipe Thermal Expansion Calculator

How much a straight pipe run grows or shrinks between a cold and a hot temperature, and the force if it were fully restrained.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A pipe changes length with temperature: ΔL = α L ΔT, where α is the coefficient of thermal expansion of the material. Carbon steel grows about 12 mm per 100 m for each 10 degrees, and stainless steel about 40 percent more.

If the pipe is not allowed to move, the growth turns into stress, σ = E α ΔT, which is far too large for the pipe or its supports. That is why pipework needs loops, offsets or expansion joints between anchors. Use the highest operating temperature for growth and the lowest shutdown temperature for contraction.

Formulas used

  • \Delta L = \alpha L \Delta T
  • \sigma = E \alpha \Delta T\ \text{(fully restrained)}

Worked example

With the default numbers in the calculator above:

  1. Temperature change: 164 K
  2. Growth of the run: 78.7 mm
  3. Per metre of pipe: 1.97 mm/m
  4. If it were fully restrained (it must not be): 394 MPa

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

How much does a steam pipe grow?

A 40 m carbon steel run from 20 to 184 degrees Celsius (10 bar steam) grows about 79 mm.

What is an anchor?

A fixed point that stops the pipe moving. The growth between two anchors must be taken up by a loop, offset or expansion joint.

Does this size the expansion joint?

No. It gives the movement. The joint, guides and anchors are an engineering design.

Related calculators

Further reading: Hibbeler, Mechanics of Materials; Gere and Goodno, Mechanics of Materials; Shigley, Mechanical Engineering Design. Crane Technical Paper 410 for pipework.

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