How to use the pressure vessel calculator
Prepare the values for this calculation
Compare the classical thin-wall hoop-stress approximation with the exact Lamé bore hoop stress for a pressurized cylindrical shell and report the radius/thickness ratio. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Unit system: choose SI — pressure in MPa, lengths in mm, US customary — pressure in psi, lengths in inches. Match this selection to the data you enter.
- Inner radius a: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
- Outer radius b: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
- Internal pressure pi: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
- External pressure po: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Exact Lamé bore hoop stress first. With the unchanged example inputs, it is 16.66666667 MPa. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Inner radius a from 50 to 55. The resulting Exact Lamé bore hoop stress is 18.67383513 MPa. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Pressure Vessel Calculator formula
Thin-wall estimate uses Δp·rm/t. Exact bore hoop stress uses Lamé theory. The comparison is educational and does not select an ASME design formula or certify code compliance.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Unit system | Select an option | SI — pressure in MPa, lengths in mm |
| Inner radius a | minimum 1e-06 | 50 |
| Outer radius b | minimum 1e-06 | 100 |
| Internal pressure pi | minimum 0 | 10 |
| External pressure po | minimum 0 | 0 |
Worked example
Using the example inputs above, the exact lamé bore hoop stress is 16.66666667 MPa.
- Exact Lamé bore hoop stress
- 16.66666667 MPa
- Thin-wall hoop estimate
- 15 MPa
- Thin vs. Lamé difference
- -10%
- Mean radius / thickness
- 1.5
- Classical model indication
- Treat as thick-walled for classical stress analysis
- Wall thickness
- 50 mm
Results and assumptions
The radius/thickness rule is an educational classification, not a design-code applicability decision. Use the governing pressure-vessel standard for real equipment design.
Sources and method references
Fix an input or unexpected result
Inner radius a is required. Enter inner radius a using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.