About this tool
The Thin-Wall Pressure Vessel Stress Calculator finds the membrane stresses in a cylindrical or spherical vessel under internal pressure, or works backwards to the wall thickness a chosen allowable stress requires. Enter the internal pressure, inside diameter and wall thickness for the stress mode, or the pressure, diameter, allowable stress and joint efficiency for the thickness mode. Pressure can be given in MPa, bar or psi and dimensions in mm or inches; everything is computed locally in your browser.
For a thin-walled cylinder (diameter-to-thickness ratio above about 20) the hoop stress is σ_h = p·r / t and the longitudinal stress is half of that, σ_l = p·r / 2t, where r is the inside radius and t the wall thickness. For a sphere the membrane stress is p·r / 2t in every direction. Solving for the required thickness gives t = p·r / (S·E) for a cylinder or t = p·r / (2·S·E) for a sphere, where S is the allowable stress and E the weld joint efficiency. The tool also reports the ASME-style minimum, t = p·r / (S·E − 0.6p) for a cylinder, which accounts for the pressure acting on the mean rather than inner radius. If the diameter-to-thickness ratio falls below 20 it flags that the thin-wall assumption no longer holds and a thick-wall (Lamé) analysis is needed.
As a worked example, a cylinder with a 500 mm inside diameter and a 6 mm wall under 2 MPa of internal pressure has a hoop stress of 2 × 250 / 6 ≈ 83.3 MPa and a longitudinal stress of about 41.7 MPa, with a diameter-to-thickness ratio of 83 — comfortably thin-walled. These formulas cover the membrane (away from ends, nozzles and supports) behaviour only; local bending at discontinuities requires additional analysis.