About Pressure Vessel Thickness Calculator
The pressure vessel thickness calculator computes the minimum wall thickness required for a cylindrical or spherical shell under internal pressure using the thin-wall rules of ASME Boiler & Pressure Vessel Code Section VIII, Division 1 (UG-27 for shells, UG-32 for formed heads). For a cylinder it evaluates both the circumferential (hoop) stress, which acts on the longitudinal seam, and the longitudinal stress, which acts on the circumferential seam, and reports which one governs.
Enter the internal design pressure P, the inside diameter D, the maximum allowable stress S for the material at design temperature, the longitudinal joint efficiency E, and a corrosion allowance. The tool returns the required thickness for each stress component, the governing minimum thickness, the total thickness including corrosion allowance, and the maximum allowable working pressure (MAWP) back-solved from the governing thickness.
How It Works
- Choose the vessel component: a cylindrical shell or a spherical shell / hemispherical head.
- Enter P (MPa), inside diameter D (mm), allowable stress S (MPa), joint efficiency E, and corrosion allowance (mm). A material selector pre-fills typical S values.
- For a cylinder the calculator applies t = P·R/(S·E − 0.6·P) for hoop stress and t = P·R/(2·S·E + 0.4·P) for longitudinal stress; for a sphere it applies t = P·R/(2·S·E − 0.2·P).
- It adds the corrosion allowance to the governing thickness and back-solves the MAWP P = S·E·t/(R + 0.6·t) (cylinder) or P = 2·S·E·t/(R + 0.2·t) (sphere), flagging any case where the thin-wall denominator goes non-positive.
Worked Example
A cylindrical SA-516 Gr 70 vessel has inside diameter D = 1000 mm (R = 500 mm), internal design pressure P = 1.5 MPa, allowable stress S = 138 MPa, joint efficiency E = 1.0, and a 3 mm corrosion allowance. Hoop thickness t = P·R/(S·E − 0.6·P) = 1.5·500/(138 − 0.9) = 750/137.1 = 5.470 mm. The longitudinal stress requires only t = 1.5·500/(2·138 + 0.6) = 750/276.6 = 2.712 mm, so hoop stress governs. Adding the 3 mm corrosion allowance gives a total required thickness of 8.470 mm. The MAWP back-solved from 5.470 mm is S·E·t/(R + 0.6·t) = 138·5.470/(500 + 3.282) = 754.9/503.28 = 1.500 MPa, confirming the design pressure.
Formulas
- Cylindrical shell — circumferential (hoop) stress thickness
t = P * R / (S * E - 0.6 * P)- Cylindrical shell — longitudinal stress thickness
t = P * R / (2 * S * E + 0.4 * P)- Spherical shell / hemispherical head thickness
t = P * R / (2 * S * E - 0.2 * P)- Maximum allowable working pressure (MAWP)
cylinder: P = S*E*t / (R + 0.6*t) | sphere: P = 2*S*E*t / (R + 0.2*t)
Standards & References
- ASME Boiler & Pressure Vessel Code, Section VIII, Division 1 (UG-27 shells, UG-32 heads)
- Thin-wall membrane theory
Frequently Asked Questions
Why does hoop (circumferential) stress govern the cylinder thickness?
In a cylinder under internal pressure the circumferential (hoop) stress is twice the longitudinal stress, so the thickness needed to resist hoop stress is larger and governs. The hoop formula t = P·R/(S·E − 0.6·P) therefore controls the shell thickness, while the longitudinal formula applies to the circumferential seams.
What is the joint efficiency E?
E is the weld joint efficiency that accounts for the reduced strength of welded seams and the degree of radiographic examination, ranging from about 0.70 for unexamined single-welded joints to 1.0 for fully radiographed double-welded butt joints. A lower E increases the required thickness proportionally.
When does the thin-wall formula stop being valid?
The ASME VIII-1 thin-wall equations apply while the wall is thin relative to the radius, roughly t/R below 0.5 (P below 0.385·S·E for the cylinder). When the denominator S·E − 0.6·P approaches zero the calculator flags the thick-wall limit, and a thick-wall (Lame) or Division 2 analysis is required.
How is the corrosion allowance handled?
The corrosion allowance is added to the governing pressure-design thickness to obtain the total nominal thickness specified for fabrication. The MAWP, however, is evaluated on the corroded (minimum) thickness so the vessel remains adequate at the end of its design life.