The second stress in a pressurised cylinder runs along its axis, pushed by the end caps: $\sigma_{l} = \dfrac{pd}{4t}$ — sigma-l equals p d over four t, where $\sigma_{l}$ is the longitudinal (axial) stress in MPa and p, d and t are the same three givens as before. Set the two side by side and the ratio is fixed for every thin cylinder ever built: $\sigma_{h} = 2\sigma_{l}$. The hoop is always double.

The reason is worth thirty seconds. Cut the cylinder lengthwise and the pressure inside is resisted by TWO strips of wall, one each side of the cut. Cut it across the girth and the end cap's push is resisted by a full ring of wall — a ring whose circumference is π d against the lengthwise cut's two thicknesses. Work the areas through and the factor of two falls out. Nothing about the material is involved; it is pure geometry.

Which is why a sausage in a pan splits along its length and never around its middle: the hoop stress reaches the skin's limit first, and a crack runs at right angles to the stress that opens it. The same fact governs a real vessel — the longitudinal weld seam carries the hoop stress and is the seam that must be perfect, while the girth seam carries half as much. When you rate a vessel, you rate the hoop. Checking the longitudinal stress is checking the easy number.