Hoop stress is the single most important number in pressure vessel design — it is the stress most likely to cause a thin-walled cylinder to fail. This calculator computes hoop and longitudinal stress from pressure, radius, and wall thickness, and can solve for thickness or pressure instead.
How hoop stress works
When a fluid or gas pushes outward against the inside of a cylindrical vessel, the wall resists in two directions at once: circumferentially (hoop stress, sigma_h = Pr/t) and along the vessel's length (longitudinal stress, sigma_l = Pr/2t). Because hoop stress is always exactly twice longitudinal stress for the same pressure, radius, and thickness, it is the value engineers check first when sizing a wall or verifying a safety margin. Both formulas assume a thin-walled cylinder with pressure applied uniformly and no external loads such as bending or fatigue.
Inputs and what they mean
Internal pressure (P) is the gauge pressure of the contents, in megapascals. Radius (r) is the inner radius of the cylinder in millimeters — using the outer radius instead introduces a small but predictable overestimate of stress. Wall thickness (t) must be strictly greater than zero; the calculator blocks a t = 0 input rather than dividing by zero. Because the formula is a simple ratio, doubling the pressure or radius doubles the stress, while doubling the thickness halves it.
Limits and edge cases
These formulas only hold for thin walls, generally t less than r/10; thicker cylinders need Lame's thick-wall equations, which this calculator does not compute, and a warning note appears when the ratio is exceeded. The calculator also does not account for stress concentrations at nozzles, welds, or end caps, corrosion allowances, temperature effects, or fatigue from repeated pressure cycles — all of which a full mechanical design review should include before finalizing a wall thickness.