Model vessel hoop stress with clear unit controls. Choose thin or thick wall assumptions instantly. Download CSV and PDF for design notes and sharing.
Thin-wall cylinder (t/ri ≤ 0.10)
Thick-wall cylinder (Lame theory)
The calculator applies joint efficiency η as a conservative adjustment: reported “η-adjusted” stresses equal stress divided by η.
| Pi (MPa) | Po (MPa) | Inner Diameter (mm) | Thickness (mm) | η | Method | Hoop Stress (MPa) |
|---|---|---|---|---|---|---|
| 2.5 | 0 | 500 | 12 | 1.00 | Thin-wall | 52.08 |
| 10 | 0 | 200 | 40 | 0.85 | Thick-wall | 69.56 (inner) |
| 5 | 0.2 | 300 | 25 | 0.90 | Auto | 31.67 (auto) |
Example results are illustrative. Always validate inputs, codes, and assumptions for your specific design case.
Hoop stress is the dominant tensile stress in many cylindrical vessels. It acts around the circumference and governs crack opening under pressure. In practical design checks, hoop stress often controls thickness, material choice, and inspection scope.
When the thickness ratio t/ri is small, stress is nearly uniform through the wall. Many engineering hand checks treat t/ri ≤ 0.10 as thin-wall. When the ratio is larger, stress varies strongly with radius and thick-wall theory is preferred.
The calculator uses the differential pressure ΔP = Pi − Po. Internal pressure may be gauge or absolute, but the difference must be consistent. External pressure can represent vacuum jackets, subsea service, or pressurized annuli.
You can enter inner diameter or inner radius. The tool converts values into an inner radius ri and an outer radius ro. Thick-wall hoop stress is highest at the inner surface for internal pressure cases, so the inner-surface selection is a conservative starting point.
Corrosion allowance reduces the effective wall thickness used in stress calculations. For example, a 10 mm wall with 2 mm allowance leaves 8 mm effective thickness. This approach supports lifecycle checks when thinning is expected or measured.
Welded joints and fabrication details can reduce effective strength. The calculator reports both unadjusted and η-adjusted stresses, where η-adjusted values equal stress divided by η. This makes comparisons against allowable or yield values more conservative and transparent.
Closed-end vessels develop longitudinal stress due to end-cap force. When enabled, the tool also estimates longitudinal stress and a von Mises equivalent stress. Von Mises provides a combined indicator when multiple principal stresses act together.
Industrial vessels often operate from tens of kPa to many MPa. Common structural steels have yield strengths roughly 250–550 MPa, while alloy steels and some stainless grades may exceed that. Always validate assumptions against your governing code and service conditions.
Auto chooses thin-wall when t/ri ≤ 0.10. Otherwise it uses thick-wall Lame equations. You can override the choice using the Method selector for conservative comparisons.
Use whichever matches your drawings. The calculator converts inner diameter to inner radius internally. Ensure the value is the inner dimension, not outside dimension, to avoid underestimating stress.
In thick walls, stress is not uniform. Lame theory predicts higher hoop stress near the inner surface under internal pressure. That is why selecting inner-surface evaluation is commonly conservative.
The tool reports η-adjusted stresses as stress divided by η. This provides a conservative comparison when weld quality or joint type reduces effective strength. Confirm how your design code applies efficiency factors.
The current calculation requires Pi > Po. For cases dominated by external pressure, buckling and collapse checks are typically required and are not covered by this hoop-stress calculator.
If you enter yield strength, safety factor equals yield strength divided by the von Mises stress. If longitudinal stress is disabled, von Mises defaults to the magnitude of the η-adjusted hoop stress.
Radial stress is compressive under internal pressure. At the inner surface it approaches −Pi, and at the outer surface it approaches −Po. This is expected behavior in pressure vessels.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.