Calculation
s = p·d/(4·σallow)
At the same pressure, diameter and material, a sphere is stressed only half as much as a cylinder and can therefore be built with a thinner wall.
Dubbel Festigkeitslehre C 5.3.1 Membrantheorie: Kugelschale σφ = σϑ = p·d/(4h)
Wall thickness of a thin-walled spherical vessel under internal pressure
At the same pressure, diameter and material, a sphere is stressed only half as much as a cylinder and can therefore be built with a thinner wall.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Required wall thickness s — Calculated minimum shell thickness with no allowances.
- Internal pressure p — Design internal pressure of the vessel.
- Inside diameter d — Inside diameter of the spherical shell.
- Allowable stress σallow — Allowable membrane stress of the material at operating temperature, including a weld-joint factor where applicable.
Example
p=16 bar, d=1,000 mm and σallow=120 MPa give s=1.6·1,000/(4·120)≈3.33 mm.
Assumptions and limits
Thin-walled spherical shell (s≪d) with no allowances for corrosion, manufacturing or weld-joint reduction; openings, nozzles, load introductions and external pressure are excluded.
Understand Wall thickness of a thin-walled spherical vessel under internal pressure
This calculator determines the required wall thickness of a spherical pressure vessel, complementing the existing calculator for cylindrical pipes with the second classic boiler formula.
What does this quantity describe?
For a thin-walled spherical shell, membrane stress is equal in every direction and half that of a cylinder's hoop stress at the same diameter and pressure: σ=p·d/(4·s), rearranged for wall thickness as s=p·d/(4·σallow).
Formula and variables
s = p·d/(4·σallow)
σ = p·d/(4·s)s = p·d/(4·σallow)
| Symbol / input | Meaning |
|---|---|
| Required wall thickness s | Calculated minimum shell thickness with no allowances. |
| Internal pressure p | Design internal pressure of the vessel. |
| Inside diameter d | Inside diameter of the spherical shell. |
| Allowable stress σallow | Allowable membrane stress of the material at operating temperature, including a weld-joint factor where applicable. |
Choose the inputs correctly
p is the design internal pressure, d the inside diameter of the spherical shell, σallow the material's allowable membrane stress.
How to use the calculator
Take p from the operating or design pressure, d from the vessel geometry, σallow from material properties at operating temperature, including a weld-joint factor where applicable.
Worked example
p=16 bar, d=1,000 mm and σallow=120 MPa give s=1.6·1,000/(4·120)≈3.33 mm.
Understand the result and units
At the same pressure, diameter and material, a sphere needs only half the wall thickness of a cylinder; this is why large pressure tanks are often built spherical.
p is a pressure, d a length, σallow a stress. s is output as a length.
Typical applications
Rough preliminary sizing of spherical pressure vessels, gas storage spheres and vessel heads with approximately spherical geometry.
Assumptions, limits and common mistakes
Thin-walled spherical shell (s≪d) with no allowances for corrosion, manufacturing tolerance or weld-joint reduction; openings, nozzles, load introductions, external pressure and the rules of a specific code (e.g. AD 2000 or EN 13445) are excluded.
Common mistake: Do not confuse the factor 4 (sphere) with the factor 2 (cylinder, hoop stress); a sphere calculated with the cylinder formula would be needlessly twice as thick.
Frequently asked questions
What is “Wall thickness of a thin-walled spherical vessel under internal pressure” used for?
Rough preliminary sizing of spherical pressure vessels, gas storage spheres and vessel heads with approximately spherical geometry.
Where do the input values come from?
p is the design internal pressure, d the inside diameter of the spherical shell, σallow the material's allowable membrane stress.
What does the result not cover?
Thin-walled spherical shell (s≪d) with no allowances for corrosion, manufacturing tolerance or weld-joint reduction; openings, nozzles, load introductions, external pressure and the rules of a specific code (e.g. AD 2000 or EN 13445) are excluded.