Pressure Vessel Calculator
Compute the minimum required wall thickness for a thin-walled cylindrical pressure vessel per the ASME hoop-stress formula, including a corrosion allowance. Used by mechanical and process engineers during vessel design and code compliance checks.
About this calculator
Thin-walled cylindrical pressure vessels are designed so that internal pressure stress does not exceed the material's allowable stress. The governing ASME formula for required wall thickness is t = (P × R) / (S × E − 0.6 × P) + C_A, where P is internal pressure, R is the inside radius, S is the allowable stress, E is joint efficiency, and C_A is the corrosion allowance. In this calculator, P is entered in bar (converted to Pa by × 100,000), diameter in mm (radius = D / 2000 in metres), S in MPa (× 10⁶), and the result is in metres. The joint efficiency factor (0–1) accounts for weld quality; a full-penetration radiographed weld typically has E = 1.0, while a spot-examined weld may use E = 0.85. Adding a corrosion allowance ensures the vessel retains structural integrity over its service life as material is gradually lost to corrosion.
How to use
Design a vessel with internal pressure P = 10 bar, internal diameter D = 500 mm, allowable stress S = 138 MPa, joint efficiency 100%, and corrosion allowance 3 mm. Step 1: Convert — P = 1,000,000 Pa; R = 0.25 m; S = 138,000,000 Pa. Step 2: Numerator = 1,000,000 × 0.25 = 250,000. Step 3: Denominator = 2 × 138,000,000 × 1.0 − 1,000,000 = 275,000,000. Step 4: t = 250,000 / 275,000,000 + 0.003 = 0.000909 + 0.003 = 0.003909 m ≈ 3.91 mm. Round up to the next standard plate thickness for fabrication.
Frequently asked questions
What is joint efficiency in a pressure vessel and how does it affect wall thickness?
Joint efficiency (E) is a reduction factor applied to the allowable stress to account for the reduced strength of welded seams compared to solid plate. A value of 1.0 (100%) applies to fully radiographed double-butt welds, while spot-examined welds typically use 0.85, and non-examined welds 0.70. A lower joint efficiency means the denominator in the thickness formula decreases, requiring a thicker wall to maintain safe stress levels. Using a high joint efficiency through rigorous weld inspection is therefore a cost-effective way to reduce material usage.
Why is a corrosion allowance added to the calculated pressure vessel wall thickness?
Corrosion allowance (C_A) is extra wall thickness included at the design stage to compensate for metal loss due to corrosion, erosion, or chemical attack over the vessel's intended service life. Typical values range from 1.5 mm for mild service to 6 mm or more for aggressive chemical environments. Without it, a vessel could become dangerously thin before its scheduled replacement or inspection. The allowance is simply added to the calculated minimum thickness and does not contribute to pressure-bearing capacity in the design calculation.
When does a pressure vessel transition from thin-wall to thick-wall design assumptions?
The thin-wall (membrane) theory applies when the wall thickness is less than about one-tenth of the vessel's inner radius (t < R/10). Beyond this threshold, the stress distribution through the wall becomes non-uniform and the simpler hoop-stress formula underestimates stress at the inner surface. Thick-wall design uses the Lamé equations, which account for radial and tangential stress gradients. For most industrial process vessels operating at moderate pressures, thin-wall theory is sufficient, but high-pressure applications like autoclave reactors or gas storage vessels often require the thick-wall approach.