Thick Wall Cylinder Stress Calculator
Calculate Lamé radial, hoop and closed-end axial stress at a radius inside a thick cylindrical wall.
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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
Use the thick-cylinder elastic pressure solution, with tensile stress positive and pressure-normal radial stress negative.
A=(pi a²−po b²)/(b²−a²); B=a²b²(pi−po)/(b²−a²); σr=A−B/r²; σθ=A+B/r²
Worked example
a=50 mm, b=100 mm, pi=10 MPa and po=0 give inner radial stress −10 MPa, inner hoop stress 16.6666667 MPa and closed-end axial stress 3.33333333 MPa.
Assumptions and input details
Uniform isotropic linear-elastic long cylinder with ideal closed ends, no thermal gradient, residual stress, yielding, buckling, stress concentration or design-code check. Query radius must be within the wall. This is not vessel certification.
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.
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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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