So far the wall has been a given and the stress the answer. A vessel designer works the other way round. The pressure is fixed by the process, the material by the service, and what has to come OUT of the arithmetic is a thickness of plate to buy. The pressure vessel code writes that direction down as one line: $t = \dfrac{PR}{SE - 0.6P}$, read aloud t equals P R over S E minus nought point six P.

The code uses capitals, so meet them properly. $t$ is the minimum required thickness of the shell in mm. $P$ is the internal design pressure in MPa. $R$ is the inside radius in mm, and the code does mean the radius, not the diameter. $S$ is the maximum allowable stress in MPa, read from the code's own table for the material and the temperature; the safety margin is already inside it, so no separate factor of safety is applied. $E$ is the joint efficiency, a bare fraction with no units that says how far the welded seam is trusted: 1.0 when it is fully radiographed, 0.85 when it is spot examined, 0.70 when it is not examined at all. Careful: this $E$ is not Young's modulus. Same letter, different chapter of the book.

Read the shape before the numbers. Cover the $E$ and the $0.6P$ and what is left is $t = PR/S$, which is the hoop formula pr/t solved for thickness. The code adds two honest corrections. $E$ multiplies $S$, so an unexamined seam is designed as though the plate were only 70 per cent as strong, and the vessel pays for skipped radiography in steel. The $-0.6P$ trims the denominator to account for the stress not being quite uniform through a real wall, and it always makes the shell a little thicker than bare thin-wall theory would.

Two things the line does not do. It is valid only while $t$ stays under half of $R$; beyond that the code sends you to thick-wall rules, which is Lamé again. And its answer is the pressure thickness only. Corrosion allowance is added on top, because the pressure thickness is what must still be there at the END of the vessel's life, and the total is then rounded UP to a plate the mill actually rolls.