Pipe Thermal Expansion and Loop Sizing

Linear expansion plus the guided-cantilever expansion-loop leg L_loop = sqrt(3 × E × D × dL / S_a).

Run the calculator

Example

You enter

Pipe material steel
Run length (ft) 200
ΔT (°F, install to operating) 100
Pipe OD (in) 4.5

You get

Linear expansion ΔL 1.56 in
Loop leg (ft) 18.73

Details, formula, and sources

Linear expansion: dL = alpha × L × dT (alpha in 1/°F). Guided-cantilever expansion loop leg: L_loop = sqrt(3 × E × D × |dL| / S_a) where E is Young's modulus (psi), D is pipe OD (in), S_a is the allowable stress (psi).

ASME B31.1 / B31.9 (Power and Building Services Piping) guided-cantilever method by name. Per-material alpha / E / S_a from data/plumbing/thermal-expansion-coefficients.json.

ASME B31 series licensed; principles free in published piping-engineering texts and at most pipe-manufacturer technical pages.

Estimate. AHJ and licensed plumber / gas fitter govern. Verify against the IPC / IFGC edition adopted in your jurisdiction.

Field names used by the API: material, length_ft, delta_T_F, pipe_OD_in, delta_L_in, loop_leg_ft

Coefficient table data/plumbing/thermal-expansion-coefficients.json keyed to materialNIST + manufacturer technical bulletins
Allowable stress S_a engineering-practice values per material (e.g., copper 5800 psi, steel A53-B 12500 psi, PEX 1500 psi)ASME B31 + manufacturer typical