Pipe Thermal Expansion Calculator

Formula overview

Temperatures in °C, α in 10⁻⁶/°C, run length in m, expansion in mm, D in mm, E and S_A in N/mm².

  ΔL    = α · (T_op − T_install) · L
  e     = α · ΔT · 10³              unit expansion, mm/m
  L_leg = √( 3·E·D·|ΔL| / S_A )     guided-cantilever leg

ASME B31.3 Appendix C tabulates total expansion directly against
temperature for common materials — that value can be entered as an
override instead of using a single average α.

Worked example

Carbon steel, installed at 20 °C, operating at 150 °C, 50 m run,
α = 11.7×10⁻⁶/°C, D = 168.3 mm, E = 203 000 N/mm², S_A = 207 N/mm²

ΔT    = 130 °C
e     = 11.7e−6 × 130 × 10³ = 1.52 mm/m
ΔL    = 1.52 × 50 = 76.1 mm
L_leg = √(3 × 203 000 × 168.3 × 76.1 / 207) = 6 136 mm ≈ 6.1 m

Movement of 76 mm at the free end — enough to matter for clearance,
hanger travel, and any branch taken off near that end.

Common mistakes

• Using a room-temperature α over a wide temperature range. The coefficient itself rises with temperature, which is exactly why B31.3 Appendix C tabulates total expansion rather than a single α — on a hot line, use the table value.
• Forgetting that austenitic stainless grows far more than carbon steel. At around 17×10⁻⁶/°C against 11.7, a stainless line moves roughly 45% further for the same temperature change and run length.
• Assuming the movement is all at one end. Where it goes depends on the anchors and guides: a run anchored at both ends does not move at all — it develops very large forces instead, which is the failure this calculation exists to prevent.

FAQ