Thin Wall Pressure Vessel Stress Calculator
Calculate ideal membrane stresses in a closed thin cylindrical or spherical shell from differential pressure, internal diameter and wall thickness.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert pressure and geometry to SI, verify the stated thin-wall ratio, then balance pressure load against uniform membrane stress. A closed cylinder has separate hoop and longitudinal stresses; a sphere has equal biaxial membrane stress.
Cylinder: σhoop=pD/(2t), σlong=pD/(4t); sphere: σ=pD/(4t)
Worked example
A closed cylinder with 1 MPa differential pressure, 1 m internal diameter and 5 mm wall has ideal hoop stress 100 MPa and longitudinal stress 50 MPa. Its radius/thickness ratio is 100.
Assumptions and input details
Requires internal radius divided by thickness greater than 10 and nonnegative differential pressure. Uniform, isotropic, linearly elastic membrane behavior and ideal closed geometry are assumed. Open ends, thick-wall gradients, nozzles, seams, weld efficiency, corrosion allowance, thermal/residual stress, fatigue, buckling, material allowables and every code requirement are excluded. This is not a vessel design or safety certification.
References: NASA Human Integration Design Handbook: thin-walled pressure-vessel stresses
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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