Pressure Vessel (Hoop Stress) Calculator
Does the wall hold? Hoop and longitudinal stress in a thin-walled cylinder or sphere, checked against the allowable — plus the minimum wall thickness and the maximum pressure the vessel can take.
Why a Pressure Vessel Splits Lengthwise
Put pressure inside a pipe or tank and the wall feels two stresses at once. The hoop (circumferential) stress tries to burst it open along its length; the longitudinal stress tries to pull the ends apart. For a cylinder the hoop stress is exactly twice the longitudinal — which is why a failed pressure vessel splits along a seam rather than popping its ends, and why the hoop direction governs the design.
p is the internal pressure, D the inside diameter and t the wall thickness. A sphere carries the pressure equally in every direction, so its wall stress is only p D / 4t — half a cylinder. That efficiency is exactly why high-pressure storage tanks are spherical.
The Decision: Thickness and Pressure
Turned around, the same relationship sizes the vessel. The minimum wall to keep the hoop stress within an allowable S is t = p D / 2S, and the most pressure a given wall can take is p = 2 S t / D. The calculator reports both, plus how much of the allowable the current design uses.
Thin Wall vs Thick Wall
These formulas assume a thin wall — a diameter-to-thickness ratio of about 20 or more — where the stress is roughly uniform through the wall. Below that, the inner surface carries noticeably more stress and you need the thick-wall (Lame) equations instead. The calculator flags when D/t drops too low.
Frequently Asked Questions
Inside or outside diameter?
Thin-wall formulas use the inside diameter (some references use the mean); the difference is small when the wall is thin, and larger differences are a sign you should switch to thick-wall analysis.
What allowable stress should I use?
Not the yield strength. Use a code allowable – typically the lesser of a fraction of yield and of ultimate (around a quarter of ultimate in ASME work), and reduce it further by the weld joint efficiency.
What about corrosion?
Add a corrosion allowance to the calculated minimum thickness so the vessel still has full wall after years of service. This tool gives the structural minimum only.
Related calculators
- Mechanical Stress Calculator — general stress, strain and safety factor.
- Pipe Flow Calculator — what is moving through the pipe.
- Pressure Drop Calculator — the pressure the line actually sees.
- Engineering Unit Converter — pressure and stress units.