Quickly model membrane stress in spherical shells. Compare operating pressure against material limits and codes. Choose units, compute thickness, and share your report easily.
For a thin-walled spherical vessel, the membrane (hoop) stress is: σ = P r / (2 t E)
Design checks use Sa/n as the allowable, where Sa is allowable stress and n is the safety factor.
| Pressure (MPa) | Radius (mm) | Thickness (mm) | Allowable (MPa) | Efficiency | Safety Factor | Membrane Stress (MPa) |
|---|---|---|---|---|---|---|
| 2.0 | 500 | 12 | 150 | 1.00 | 1.50 | 41.666667 |
| 5.0 | 300 | 10 | 200 | 0.85 | 2.00 | 88.235294 |
| 1.2 | 1000 | 16 | 160 | 1.00 | 1.25 | 37.500000 |
A thin spherical pressure vessel develops a uniform membrane stress in its wall. Because the curvature is the same in every direction, the stress state is simpler than for cylinders. This calculator focuses on the classic thin-wall model used for quick sizing, checks, and sensitivity studies. It also helps compare design margins across multiple operating scenarios.
The thin-wall assumption is typically reasonable when wall thickness is small compared with the inner radius. As a practical screening rule, many engineers start with t/r ≤ 0.1 and then refine with more detailed methods when the ratio grows. Use this tool for preliminary assessments, not final code compliance.
Internal pressure, inner radius, and wall thickness control the membrane stress. Pressure scales stress linearly, radius increases stress, and thickness reduces stress. The optional weld or joint efficiency reduces the effective thickness, and the allowable stress plus safety factor provide a quick pass/fail indication.
For a spherical vessel under internal pressure, the membrane (hoop) stress is σ = P·r/(2·t). In consistent units, σ is expressed in pressure units (Pa or MPa). For example, P = 2 MPa, r = 500 mm, and t = 12 mm gives σ ≈ 41.7 MPa.
Allowable stress depends on material, temperature, and design basis. This calculator lets you compare the computed membrane stress against a design allowable adjusted by a safety factor: allowable_design = allowable / n. If efficiency is less than 1.0, the stress increases because the effective thickness is reduced.
The form accepts common engineering units and converts them internally to a consistent SI basis before calculating. Pressure options include Pa, kPa, bar, psi, and MPa; length options include mm, cm, m, in, and ft. Results are displayed in MPa by default for readability.
The reported membrane stress represents an average through-wall stress in the thin-wall idealization. It does not capture local peaks near nozzles, supports, weld toes, or geometric discontinuities. If the stress is close to the allowable, treat it as a flag to perform a more detailed analysis.
Typical uses include estimating required thickness for a target pressure, checking the impact of radius changes, and comparing alternative materials or fabrication efficiencies. Engineers also use quick calculations to validate simulation outputs. Always confirm that loading, corrosion allowance, and temperature effects are properly addressed.
In the thin-wall model, a spherical vessel has a single uniform membrane stress in the wall due to internal pressure. It is the same in all tangential directions around the sphere.
The spherical geometry shares the pressure load over two orthogonal membrane directions, so the membrane stress is lower than in a thin cylinder for the same pressure, radius, and thickness.
If thickness is not small compared with radius, or if you need through-thickness stress distributions, use a thick-wall solution or numerical analysis. Discontinuities and openings also require refined methods.
Efficiency reduces the effective strength or thickness available to carry load. In this calculator, it acts as a multiplier on thickness, increasing computed stress when efficiency is less than 1.0.
Not automatically. If you have a corrosion allowance, subtract it from the nominal thickness to get an effective thickness, then enter that effective thickness into the calculator.
This tool is for internal pressure membrane stress. External pressure typically governs buckling and requires different criteria and equations, so do not use this output for collapse checks.
Finite element models capture local stress concentrations from geometry, boundary conditions, and load paths. This calculator reports the idealized membrane stress, which is often lower than peak stresses.
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.