How to use this calculator
Choose a cylinder or sphere, then enter the gauge pressure, the inside diameter and the wall thickness. The calculator checks that the wall is thin enough (r/t ≥ 10) for these formulas to apply.
Formulas
Worked example
Cylinder, 1 m diameter, 10 mm wall, 2 MPa (the default)
- r = 500 mm, so r/t = 50: the thin-wall formulas apply.
- σh = 2 × 500 / 10 = 100 MPa.
- σl = 2 × 500 / 20 = 50 MPa.
- σvm = √(100² − 100 × 50 + 50²) = 86.6 MPa, so n = 260 / 86.6 = 3.0.
A sphere of the same size and wall has half the hoop stress, which is why gas storage tanks are often spherical.
Assumptions and limits
- The wall is thin: r/t of at least about 10.
- Stresses are away from heads, nozzles and supports, where bending adds to them.
- Radial stress through the wall is ignored (it is at most p, small next to the hoop stress).
- Pressure is gauge pressure: the difference between inside and outside.
Frequently asked questions
Why is the hoop stress twice the longitudinal stress?
Cut the cylinder lengthwise and the pressure acts on a projected area of 2rL, resisted by two walls of area tL. Cut it crosswise and the pressure acts on πr², resisted by a ring of area 2πrt. The algebra gives pr/t and pr/2t.
Should r be the inside or mean radius?
Textbooks use either. The inside radius is slightly conservative and matches the ASME approach for thin shells; the difference is small when r/t is large.
What if the wall is thick?
Use the Lamé thick-wall equations, which give the stress varying through the wall with its maximum at the inner surface.
For education and preliminary checks only. Have a qualified engineer verify any design before it is built.