SettingsSettings for this calculationUS
The pipe material, which sets both the stiffness and the allowable bending stress.
This is the single biggest driver of loop size and it is not a detail: a copper loop is roughly 40% longer than a carbon steel one for the same movement, and a PVC loop about a third of the steel length. The figures in each option are nominal ambient-temperature properties. Allowable stress falls with temperature, so a high-temperature line should be re-checked against the code allowable at its own design temperature.
The pipe's outside diameter.
Use the actual outside diameter (OD) of the pipe, not its nominal size, if the two differ for your pipe material.
The total linear thermal expansion the pipe run is expected to undergo.
Calculate this from the pipe material's coefficient of thermal expansion, the anchored run length, and the expected temperature swing between installation and operating conditions.
Required loop leg length
15.5 ft
This simplified formula is a commonly-used approximation for preliminary sizing — final expansion loop design should be verified against the pipe manufacturer's or ASME B31 piping code stress analysis for critical or high-temperature systems.
- Modulus of elasticity used (psi)
- 29,000,000 psi
- Allowable bending stress used (psi)
- 20,000 psi
They open the calculator with your figures already in it
Pipe Thermal Expansion Loop Sizing Calculator: 15.55 ft — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Simplified expansion loop sizing: L(in) = √(3 · E · Do(in) · ΔL(in) / σ), the guided-cantilever relation for sizing a square/U-shaped expansion loop's leg length from the pipe's outside diameter and expected linear expansion, keeping bending stress within allowable limits
Inputs used
- Pipe Material
- Carbon steel (29,000 ksi, 20 ksi allowable)
- Pipe Outside Diameter
- 4 in
- Expected Linear Expansion
- 2 in
Intermediate steps
- Modulus of elasticity used (psi)
- 29,000,000 psi
- Allowable bending stress used (psi)
- 20,000 psi
Confidence note: This simplified formula is a commonly-used approximation for preliminary sizing — final expansion loop design should be verified against the pipe manufacturer's or ASME B31 piping code stress analysis for critical or high-temperature systems.
What this calculation does not cover
- Sizes the loop and not the anchors that make it work. A loop only absorbs movement if the run is anchored at both ends and guided on the approach, and that anchor then has to hold what the loop pushes back with - the spring force of the legs, the friction of every guide, and pressure thrust wherever the line is not axially restrained. On a hot steel main that reaction can run to thousands of pounds, a tonne or more, so a strut frame or stanchion sized by eye is the part that lets go first, with the loop still looking perfectly correct.
- The answer is ONE LEG. A square loop is two legs plus the width between them, commonly taken as about half the leg, so the pipe, the insulation, the fluid and the space needed in a ceiling void or a trench are all larger than this dimension suggests. The developed pipe added to the run - roughly two legs plus that width - also adds pressure drop, extra fluid volume and, on a steam line, another low point that has to be drained.
- Supports on and around the loop must let it move. A rigid hanger, a hard clamp or a bearing point on a loop leg installs a restraint exactly where the pipe is meant to flex, and the movement that stops going into the loop goes into branch connections, equipment nozzles and anchors instead. Loop legs are carried on slides, rollers or hangers with enough swing, and the guides on the straight runs are there to stop the pipe buckling sideways, not to hold it still.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-06 · in the site-wide review of 2026-09-06 · v1.1.0
Regulatory standards & verification citations1
- Simplified expansion loop sizing: L(in) = √(3 · E · Do(in) · ΔL(in) / σ), the guided-cantilever relation for sizing a square/U-shaped expansion loop's leg length from the pipe's outside diameter and expected linear expansion, keeping bending stress within allowable limits
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Tools and safety for this job
To cut and prepare copper pipe and cut and join plastic pipe. Generic types, no brands, no prices.
Protection this work requires
- Knives cause more site injuries than any power tool: cut away from your body, change blades often, and wear cut-resistant gloves to EN 388 level C for repeated cutting.
Cut and prepare copper pipe: Cutting and joining pipe is within reach of a competent DIYer; the system it joins may not be. Work on a gas supply, an unvented cylinder, or a sealed heating system is restricted to a registered installer in most markets, and a tool list is not a qualification.
Cut and join plastic pipe: Push-fit and solvent-weld plumbing is within reach of a competent DIYer. The regulated parts of the system — gas, unvented hot water, and anything notifiable — are not, whatever tools are to hand.
Show the 5 tools this job needsHide tools
Essential
Copper pipe cutter
Deburring tool and wire wool
Plastic pipe shears
Tape measure
Recommended
Adjustable spanner and grips
Also needed as materials: cutting wheels.
what each plumbing tool is for, and the spec that decides which to buy where one does.