Thin-Wall Pressure Vessel Stress Calculator (Cylinder and Sphere)
Hoop and longitudinal stress in a thin-walled cylinder or sphere under internal pressure, the wall thickness needed for an allowable stress, and the highest pressure a given wall can take.
Results
What this tool does
In a pressurised cylinder the stress around the circumference is twice the stress along the axis, σ = pr ÷ t against pr ÷ 2t — which is why a sausage splits lengthwise and a boiler seam along the length is the one that matters. A sphere carries the pressure with half the wall of a cylinder of the same size, at pr ÷ 2t in every direction. The formulas hold when the radius is at least about ten times the wall. Real pressure-vessel codes add a corrosion allowance, safety factors and tested joint efficiencies, so use this for a first estimate, not for certification.
Formula
hoop σ = p r ÷ t · longitudinal σ = p r ÷ 2t (cylinder, and sphere) · t_needed = p r ÷ (S E) · valid when r ≥ 10 t
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pb | Internal pressure (gauge) | bar |
di | Inside diameter | mm |
tw | Wall thickness | mm |
sa | Allowable stress of the material | MPa |
ej | Weld joint efficiency (1 = seamless) | — |
HO | Hoop stress (around the circumference) | MPa |
LO | Longitudinal stress (along the axis; also a sphere's stress) | MPa |
UT | Share of the allowable stress used | % |
TR | Wall thickness needed | mm |
PM | Highest pressure this wall allows | bar |
VD | Thin-wall formulas valid? | — |
Worked example
- Internal pressure (gauge)10 bar
- Inside diameter500 mm
- Wall thickness5 mm
- Allowable stress of the material120 MPa
- Weld joint efficiency (1 = seamless)1
- Hoop stress (around the circumference)50.0 MPa
- Longitudinal stress (along the axis; also a sphere's stress)25.0 MPa
- Share of the allowable stress used42 %
- Wall thickness needed2.08 mm
- Highest pressure this wall allows24.0 bar
- Thin-wall formulas valid?Yes — radius is at least 10 times the wall
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.