Hoop Stress Calculator
Calculate hoop (circumferential) stress in a thin-walled pipe or pressure vessel from internal pressure, diameter, and wall thickness.
How this calculator works
When a pipe or pressure vessel holds pressure inside, that pressure pushes outward against the wall in every direction around the circumference. This calculator takes the internal pressure, the pipe diameter, and the wall thickness, then finds the hoop stress — the stress trying to stretch the wall around its circumference.
Formula: Hoop stress = (Internal pressure × Diameter) ÷ (2 × Wall thickness). This is the standard thin-wall pressure vessel formula, valid when wall thickness is small relative to diameter, roughly under 1/10.
Worked example
150 psi internal pressure, a 12-inch diameter pipe, and a 0.25-inch wall thickness:
- Internal pressure: 150 psi
- Diameter: 12 in
- Wall thickness: 0.25 in
- Hoop stress: (150 × 12) ÷ (2 × 0.25) = 1,800 ÷ 0.5 = 3,600 psi
Notes
Hoop stress is the circumferential (around-the-pipe) stress from internal pressure trying to burst the pipe outward. It is typically about twice the pipe’s longitudinal (lengthwise) stress under the same pressure, which is why pressure vessel failures tend to split lengthwise along the pipe rather than crack across it.
This formula applies to thin-walled pipes and vessels, where the wall thickness is small compared to the diameter. Compare the result against your pipe material’s allowable stress to check whether the wall thickness is adequate for the pressure it will see.
How to use
Enter the internal pressure, the pipe’s outer or nominal diameter, and the wall thickness, all in consistent units. The calculator returns the hoop stress in psi, which you can compare against the pipe material’s allowable stress to confirm the wall is thick enough for the application.
This is a planning estimate using standard mechanics-of-materials formulas, not a substitute for engineering design. Confirm actual stress limits and material allowables with a licensed structural or mechanical engineer.
Frequently asked questions
What is hoop stress?
Hoop stress is the stress that runs around the circumference of a pipe or pressure vessel, caused by internal pressure pushing outward against the wall. Picture a barrel hoop wrapped around a cask — the pressure inside tries to stretch that hoop, and hoop stress is how hard the wall material has to resist that stretch.
Why does hoop stress matter for pipe failures?
Hoop stress is typically about twice the pipe's longitudinal (lengthwise) stress under the same internal pressure. Because the circumferential direction is under more stress, pressure vessel and pipe failures tend to split lengthwise along the pipe rather than crack straight across it. Knowing the hoop stress is usually the governing check for pipe wall thickness.
What does thin-walled mean for this formula?
This formula assumes the pipe wall is thin relative to its diameter, roughly under one-tenth of the diameter. Under that condition, stress is treated as roughly uniform through the wall thickness. Thicker-walled pipes and vessels need more detailed thick-wall equations that account for stress variation from the inner to the outer surface.
How do I know if my pipe's wall thickness is adequate?
Compare the calculated hoop stress against your pipe material's allowable stress, which comes from a materials spec sheet or piping code. If the hoop stress is comfortably below that allowable, with the safety margin your application requires, the wall thickness is likely adequate — confirm with a qualified engineer for anything pressure-critical.
Estimates only. Verify quantities with your supplier before purchasing.