Pressure Vessel Design Calculator
Minimum shell and head thickness for an internal-pressure vessel per ASME Section VIII Division 1, with corrosion allowance and the next standard plate.
When to use this calculator
Use for sizing a cylindrical shell or a formed head under internal pressure at the specification or check stage — putting a first thickness on a vessel sketch, verifying a fabricator's proposal, or seeing how much a change in material or joint efficiency actually buys. It applies the three thin-wall membrane rules of ASME VIII-1: UG-27(c)(1) for the shell, UG-32(f) for a hemispherical head, and UG-32(d) for a 2:1 ellipsoidal head, then adds the corrosion allowance and rounds up to the next commercial plate.
Required inputs
- Component — cylindrical shell, hemispherical head, or 2:1 ellipsoidal head
- Design pressure P and inside diameter D
- Allowable stress S at design temperature (ASME II-D)
- Joint efficiency E per UW-12, from the degree of radiography
- Corrosion allowance c
Expected outputs
- Pressure thickness, before corrosion allowance
- Required thickness t + c
- Next standard plate thickness
- Thin-wall validity check against P ≤ 0.385·S·E
Formula overview
SI and consistent: P and S in MPa, D, R, t, and c in mm. E is dimensionless, between 0 and 1. Standard plates run 3, 4, 5, 6, 8, 10, 12 … 60 mm.
ASME BPVC Section VIII, Division 1 — internal pressure:
Shell, circumferential stress UG-27(c)(1)
t = P·R / (S·E − 0.6·P) R = inside radius
Hemispherical head UG-32(f)
t = P·R / (2·S·E − 0.2·P) R = inside radius
2:1 ellipsoidal head UG-32(d)
t = P·D / (2·S·E − 0.2·P) D = inside DIAMETER
then t_required = t + c, rounded up to the next standard plate.
Thin-wall membrane rules are valid only while P ≤ 0.385·S·E.Worked example
Vessel with P = 1.5 MPa, inside diameter D = 2000 mm, S = 138 MPa,
E = 0.85 (spot radiographed), corrosion allowance c = 3 mm
Thin-wall limit: 0.385 × 138 × 0.85 = 45.2 MPa ≫ 1.5 MPa → valid
Shell, R = 1000 mm:
t = 1.5 × 1000 / (138 × 0.85 − 0.6 × 1.5)
= 1500 / 116.4 = 12.89 mm → +3 = 15.89 → 16 mm plate
2:1 ellipsoidal head, D = 2000 mm:
t = 1.5 × 2000 / (2 × 117.3 − 0.3)
= 3000 / 234.3 = 12.80 mm → +3 = 15.80 → 16 mm plateCommon mistakes
- Swapping radius and diameter between the rules. The shell and hemispherical formulas take the inside radius; the 2:1 ellipsoidal head formula takes the inside diameter. Using D where R belongs doubles the answer, and it is the single most common error on this calculation.
- Leaving E at 1.0 without the radiography to justify it. UW-12 ties joint efficiency to the examination actually performed — full radiography earns 1.0, spot 0.85, and none 0.70 for a double-welded butt joint. Choosing E is a fabrication and inspection commitment, not a free parameter.
- Ignoring the thin-wall limit. Once P exceeds 0.385·S·E these membrane rules no longer apply and the vessel needs the thick-wall treatment of Appendix 1-2 instead.
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