What is the difference between hoop stress and longitudinal stress?

Hoop stress (circumferential stress) acts around the circumference of a cylindrical pressure vessel and is typically twice the longitudinal stress, which acts along the vessel's axis. For thin-walled cylinders under internal pressure, σ_hoop = P·r/t and σ_longitudinal = P·r/(2t).

How does joint efficiency affect required wall thickness?

Joint efficiency (E) accounts for weld quality and inspection level per ASME UW-12. A lower E value (e.g., 0.7 for spot-examined welds vs. 1.0 for fully radiographed) increases the required wall thickness because the formula divides by E, making the denominator smaller.

When should a corrosion allowance be added?

A corrosion allowance should be added when the vessel contents or environment will cause wall thinning over time. The allowance (typically 1/16" to 1/8" for carbon steel) is added to the calculated minimum thickness. The vessel must pass all stress checks at the corroded thickness (t - CA).

Engineering DisclaimerEngineering calculations are provided for preliminary design and educational/reference purposes only. Users must verify all results according to applicable engineering standards, supplier data, manufacturing requirements, and professional engineering judgment.

ASME BPVC VIII-1

Machine Design

Pressure vessel wall thickness is the minimum wall thickness required to contain a given internal pressure. Use the formula t = PD / (2 × SE − P) where P = operating pressure, D = inside diameter, SE = allowable stress × weld joint efficiency per ASME Section VIII.

Pressure Vessel Wall Thickness Calculator

Calculate minimum required wall thickness for cylindrical and spherical pressure vessels per ASME BPVC Section VIII Division 1, including circumferential (hoop), longitudinal, and membrane stress checks with joint efficiency and corrosion allowance.

Unit System

Input Parameters

Vessel Shape

Design Pressure (P) — MPa

MPa

Inside Radius (R) — mm

Allowable Stress (S) — MPa

MPa

Joint Efficiency (E)

Corrosion Allowance (CA) — mm

Calculation Summary

Input Parameters

Design Pressure (P)	1.50MPa
Inside Radius (R)	500.0mm
Joint Efficiency (E)	1.0

Calculated Results

Required Thickness	5.47mm KEY
Total Thickness (+ CA)	8.47mm
Circumferential Stress	137.10MPa
Longitudinal Stress	68.55MPa

Mathematical Models & Equations

Governing Equation

Cylindrical circumferential (UG-27): t = P·R / (S·E − 0.6·P)

Cylindrical Circumferential

t = P·R / (S·E − 0.6·P)

Cylindrical Longitudinal

t = P·R / (2·S·E + 0.4·P)

Verification Calculation Log

1Compute circumferential (hoop) thickness: t = P·R / (S·E − 0.6·P) = 1.5 × 500 / (138 × 1 − 0.6 × 1.5)
2Compute longitudinal (axial) thickness: t = P·R / (2·S·E + 0.4·P) = 1.5 × 500 / (2 × 138 × 1 + 0.4 × 1.5)
3Governing thickness = the larger of the two per UG-27: 5.47
4Hoop stress at required thickness: σ = P·R / t = 137.10
5Longitudinal stress at required thickness: σ = P·R / (2·t) = 68.55
6Add corrosion allowance: t_total = 5.47 + 3 = 8.47

Engineering Application Notes

Formulas per ASME BPVC Section VIII Div. 1, UG-27 — thin-walled shells. Governing thickness is the LARGEST of the applicable formulas. Joint efficiency E per UW-12 depends on radiography extent. Always add corrosion allowance to the code-required thickness. Nozzles, openings, and heads require additional reinforcement checks per UG-36 to UG-45. Hydrostatic test pressure per UG-99 should be verified before fabrication.

Standard Citations & References

ASME Boiler and Pressure Vessel Code, Section VIII Division 1

ASME BPVC VIII-1

UG-27 (thin-wall shells), UG-28 (thick-wall), UG-33, UW-12 (joint efficiency).

ASME Section II Part D — Material Properties

ASME II-D

Maximum allowable stress values S for pressure-retaining materials at design temperature.

Domain of Validity

Valid for cylindrical pressure vessels with internal pressure per ASME BPVC Section VIII Division 1. Applies to inside radius to thickness ratio greater than 10. Not valid for external pressure, vacuum, or thick-walled vessels (r/t less than 10).

Worked Example

SA-516 Gr. 70 vessel, P = 10 bar, D = 1000 mm, S = 120 MPa, E = 1.0: t = (P x D) / (2 x S x E - P) = (10 x 1000) / (2 x 120000 x 1.0 - 10) = 5.01 mm. With 2 mm corrosion allowance: t_total = 7.01 mm.

Verification

ASME BPVC Section VIII Division 1 UG-27 verified formula. Last verified: August 2026.

Accuracy and Uncertainty

Wall thickness calculation has plus/minus 5% uncertainty due to material property variation and weld joint efficiency assumptions. Always apply corrosion allowance for chemical service.

Frequently Asked Questions

What is the minimum wall thickness for pressure vessels?

ASME BPVC Section VIII requires a minimum manufactured wall thickness of 3.18 mm (0.125 in) for unfired pressure vessels. For chemical service, a corrosion allowance of 3-6 mm is typically added.

What is the stress allowable value (S)?

The allowable stress (S) is from ASME BPVC Section II Part D Table 1A. It depends on material grade and design temperature. For SA-516 Gr. 70 at 20 C, S = 120 MPa.

What is weld joint efficiency (E)?

Weld joint efficiency (E) is the ratio of joint strength to base metal strength. Values: E = 1.0 for full radiography, E = 0.85 for partial radiography, E = 0.70 for no radiography (ASME UW-12).

Can this calculator handle external pressure?

No. External pressure (vacuum) uses a different formula based on ASME BPVC Section VIII UG-28. The cylindrical shell formula for external pressure considers buckling, not tensile stress.

What ASME code does this use?

ASME BPVC Section VIII Division 1, UG-27 for internal pressure. For lethal service, see UCS-66 and UCS-67 stress limits.