Mechanical & Civil Engineering
Thick-Walled Cylinder Lamé Equations Calculator
Compute radial and hoop stresses in a thick-walled cylinder using Lamé's equations.
Your inputs
Change any value to update the result instantly.
Hoop stress at inner radius
33.333 MPa
Radial stress at inner radius
-20 MPa
Hoop stress at outer radius
13.333 MPa
Wall ratio ro/ri
2
What this calculator does
Thick-Walled Cylinder Lamé Equations Calculator: Applies the standard mechanics-of-materials relationship for this load case so a student can see how the stress, strain or deflection follows from the geometry and the load.
What your result means
The headline figure tells you how hard the material is being worked, or how much it moves, under the load you entered. Compare it with the allowable value for your material and required factor of safety.
Formula and working
σh = (pi·ri² - po·ro² - (pi-po)ri²ro²/r²) / (ro² - ri²)
- 1
Collect the inputs
Inner radius = 50 mm; Outer radius = 100 mm; Internal pressure = 20 MPa; External pressure = 0 MPa
- 2
Apply the formula
σh = (pi·ri² - po·ro² - (pi-po)ri²ro²/r²) / (ro² - ri²)
- 3
Result
Hoop stress at inner radius = 33.333 MPa
Frequently asked questions
Symbols and assumptions
- ri
- Inner radius (mm)
- ro
- Outer radius (mm)
- pi
- Internal pressure (MPa)
- po
- External pressure (MPa)
- • The material is homogeneous, isotropic and loaded within its linear-elastic range.
- • Inputs are entered in a consistent unit system, as labelled on each field.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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