Pressure Vessel Wall Thickness Calculation: Worked Example

Last updated: 2026-10-17 · Reviewed by: Senior Metallurgical Engineer, {BRAND}

A 3.0 m inside diameter shell at 1.6 MPa design pressure in SA-516 Grade 70 needs 17.5 mm of pressure thickness by UG-27, and 20.5 mm once 3 mm of corrosion allowance is added, so it is ordered as 22 mm plate. The formula is t = P·R / (S·E − 0.6·P); the answer is set by four numbers — allowable stress, joint efficiency, design pressure and radius — and by a fifth, the corrosion allowance, which usually determines the plate you actually buy.

Key Takeaways

• UG-27 gives the pressure thickness; corrosion allowance and minimum thickness are added afterwards, never before.
• Joint efficiency is a design decision: E = 1.0 with full radiography can save 3 mm of wall at 3 m diameter.
• Round the calculated thickness up to available plate, then check it against the minimum thickness rules.
• MAWP is calculated from the thickness you actually have, minus allowance, and it is not the design pressure.
• Each millimetre of wall on a 3 m × 6 m shell is about 0.44 t of steel, roughly USD 800 of plate.

What Is the Wall Thickness Formula and Where Does It Come From?

The circumferential stress formula in ASME Section VIII Division 1 UG-27(c)(1) is t = P·R / (S·E − 0.6·P), where t is the minimum required thickness, P is internal design pressure, R is inside radius, S is maximum allowable stress and E is joint efficiency. It comes from a thin-wall hoop stress balance with a correction term for the fact that the wall is not infinitely thin.

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Hoop stress is a tensile stress that acts around the circumference of a cylindrical shell and is roughly twice the longitudinal stress at the same pressure, which is why circumferential seams govern shell thickness and why longitudinal seams govern the thickness of a pipe under pressure.

Joint efficiency (E) is a factor that reduces allowable stress to account for welded joints whose quality has not been proven by full radiography. In Division 1, UW-12 assigns E by joint type and degree of examination: full radiography on a double-welded butt joint gives E = 1.0, spot radiography gives 0.85, and no radiography gives 0.70 for the same joint.

Maximum allowable working pressure (MAWP) is the highest internal pressure at the top of the vessel, in its operating position, at the design temperature, based on the thickness actually present and corroded to the next inspection interval. It is calculated from the same equation rearranged, and it is what the relief valve is set from.

Corrosion allowance (CA) is a thickness that is added to the pressure thickness to cover metal loss over the design life. It is added after the code calculation, not inside it, because the code is calculating the thickness needed to hold pressure on the day the vessel is new.

A pressure vessel wall thickness calculation therefore has one purpose: to establish the minimum metal that will hold the design pressure at the design temperature on the worst day of the vessel’s life, with the examination level the specification actually funds. Everything else on the drawing — the allowance, the rounding, the forming allowance — is an addition to that number.

The distinction between these quantities matters because they are frequently conflated on drawings. A vessel with a 22 mm shell, a 3 mm allowance and a 19 mm minimum measured thickness has a remaining pressure thickness of 19 mm, and its MAWP is calculated on 19 mm — not on the 22 mm ordered, and not on the 20.5 mm calculated. Inspection reports that quote “thickness above minimum” without stating which minimum they mean are the source of most re-rating disputes.

Which Inputs Go Into the Calculation?

Table 1 lists the inputs, where each comes from, and the error that each most often carries. A pressure vessel wall thickness calculation is only as good as these inputs; the arithmetic itself is trivial, and the engineering judgement lives entirely in the eight rows below.

Table 1 — Inputs to a Division 1 shell thickness calculation

Two rows deserve elaboration because they cause most of the rework. Design pressure must include the static head of liquid above the point being calculated and any pump dead-head or relief valve set pressure that can be imposed. A leaching tank with 8 m of slurry above the nozzle sees about 0.08 MPa of additional pressure at the bottom, which is small against 1.6 MPa but not against 0.3 MPa. Design temperature must include the excursion case: a pressure oxidation autoclave that runs at 210 °C but sees 230 °C during an upset has to use the allowable stress at 230 °C, and the difference between 125 MPa and 118 MPa is 3 mm of wall at 4 m diameter.

Worked Example 1: Cylindrical Shell Under Internal Pressure

Take a leach feed tank: inside diameter 3,000 mm, design pressure 1.6 MPa, design temperature 60 °C, material SA-516 Grade 70, full radiography of all seams, corrosion allowance 3 mm.

Step 1 — Fix the geometry. R = 1,500 mm (inside radius).

Step 2 — Read the allowable stress. From Section II Part D at 60 °C, SA-516 Grade 70 gives S = 138 MPa. The value is read at design temperature, not at ambient.

Step 3 — Set joint efficiency. With full radiography on all double-welded butt joints, E = 1.0.

Step 4 — Apply UG-27(c)(1).

t = P·R / (S·E − 0.6·P)
= 1.6 × 1,500 / (138 × 1.0 − 0.6 × 1.6)
= 2,400 / 137.04
= 17.51 mm

Step 5 — Add corrosion allowance. 17.51 + 3.0 = 20.51 mm.

Step 6 — Round to available plate. The next standard thickness is 22 mm. Order 22 mm, and check that mill tolerance does not take the delivered plate below 20.51 mm; for a 22 mm plate with a 0.3 mm under-tolerance the minimum delivered is 21.7 mm, which is acceptable.

Step 7 — Check minimum thickness. UG-16 requires 1.5 mm for carbon steel pressure-retaining plate, so 22 mm is comfortably above it. The practical minimum in most fabricators’ standards for a 3 m shell is higher — 6 to 8 mm — for handling and out-of-roundness.

Now change one input and watch the answer move. If the specification allows spot radiography instead of full, E = 0.85:

t = 1.6 × 1,500 / (138 × 0.85 − 0.96)
= 2,400 / 116.34
= 20.63 mm

Adding 3 mm gives 23.63 mm, which rounds to 25 mm. The decision to save radiographic cost has added 3 mm of wall on every square metre of shell, which on this vessel is about 1.3 t of steel — considerably more than the radiography would have cost. That is the single most useful calculation in this article, and the reason full radiography is almost always the right specification for vessels above about 2 m diameter.

Worked Example 2: 2:1 Ellipsoidal Head

The same vessel needs a head. For a 2:1 ellipsoidal head under internal pressure, Division 1 UG-32(d) gives t = P·D / (2·S·E − 0.2·P), where D is the inside diameter of the head skirt.

t = 1.6 × 3,000 / (2 × 138 × 1.0 − 0.2 × 1.6)
= 4,800 / 275.68
= 17.41 mm

Adding 3 mm of corrosion allowance gives 20.41 mm, which rounds to 22 mm — the same plate as the shell, a small procurement advantage worth having. Two corrections are then applied on top:

1. Forming thinning allowance. Cold-formed ellipsoidal heads thin at the crown and knuckle by roughly 8–12% of nominal thickness depending on forming method and head size. The ordered plate thickness is increased so the thinnest point after forming still meets the calculated requirement, which here means ordering 24 mm rather than 22 mm.
2. Knuckle buckling check. The knuckle region is in compression on the inside surface and can buckle; Division 1 handles this through the rules in UG-32 and the thickness limits, and very large or very thin heads may need a design-by-analysis check.

For a smaller vessel the head often governs rather than the shell, because the head formula has a 2 in the denominator but the diameter term is the full diameter rather than the radius, and the forming allowance pushes the ordered plate up one size. Checking both and ordering the thicker plate is routine; specifying the shell thickness and letting the head follow is how fabricators end up buying two plate sizes for one vessel.

Worked Example 3: MAWP and Hydrotest Pressure

Once the vessel exists, the question changes from “how thick does it need to be” to “what pressure can it hold”. Rearranging UG-27 gives the MAWP for the measured thickness:

MAWP = S·E·(t − CA) / (R + 0.6·(t − CA))

For the 22 mm shell above, after 10 years of service with measured thickness of 20.1 mm and a remaining allowance of 1.6 mm above the 19.5 mm minimum:

t_effective = 20.1 mm
MAWP = 138 × 1.0 × 20.1 / (1,500 + 0.6 × 20.1)
= 2,773.8 / 1,512.1
= 1.83 MPa

The MAWP of 1.83 MPa is above the 1.6 MPa design pressure, so the vessel remains fit for its design duty. If measured thickness had been 19.0 mm the MAWP would fall to 1.73 MPa, still above design but with little margin — and at that point the correct action is to re-rate, reduce the relief valve setting, or plan replacement, not to keep operating on the original nameplate.

The same rearrangement applies to equipment that is a pressure vessel without looking like one. The plate pack of a filter press is a pressure-retaining assembly whose rating is set by the frame, the plate thickness and the sealing pressure, and the filtration pressure quoted in a specification is an operating parameter rather than a design rating. Confusing the two is how a filter press ends up operated above the pressure its plates were designed for.

Hydrotest pressure in UG-99(b) is calculated as 1.3 × MAWP × (S_test / S_design), where S_test is the allowable stress at the test temperature. For a new vessel with MAWP equal to design pressure of 1.6 MPa and no stress-ratio correction:

P_test = 1.3 × 1.6 × 1.0 = 2.08 MPa

The test is performed at the test temperature with the stress ratio applied, and the vessel is examined at that pressure. Two practical notes: the hydrotest pressure must not be applied to a vessel whose supports were designed only for operating weight plus liquid, and the test water chloride content matters for stainless vessels — a hydrotest with 200 mg/L chloride water left to dry in a 316L vessel can initiate pitting before the vessel ever sees process liquor.

What Do Rounding, Minimum Thickness and Mill Tolerance Add?

The calculation produces a number with two decimal places; the vessel is built from plate that exists in 2 mm increments and arrives slightly under nominal. Three adjustments sit between the calculation and the purchase order.

Table 2 — Adjustments between calculated and ordered thickness

The mill tolerance point is more important than it looks. A vessel calculated at 20.51 mm and ordered at 21 mm would be non-compliant on delivery if the plate came in 0.3 mm under, and the fabricator would have to reject the plate or seek a deviation. Ordering the next standard size above calculation plus allowance avoids the argument entirely, and the cost of one plate increment is small against a rejected shell course.

The same logic applies to nozzle reinforcement. UG-37 area replacement requires that material removed by the opening be replaced by excess thickness in the shell, in the nozzle neck, or in a reinforcing pad. A nozzle that removes 3 mm of shell in an area where the shell is only 1.5 mm above minimum has no excess to contribute, and the pad has to make up the whole difference — which is why nozzle schedules on thin-walled stainless vessels often look heavier than the shell.

A clad or overlay vessel adds one further step, and it is the one most often omitted. The pressure thickness is carried entirely by the base metal; the weld overlay or clad layer is a corrosion barrier and is not counted as pressure-retaining thickness, even though it appears on the drawing as part of the wall. The calculation therefore uses the base metal thickness only, and the overlay thickness is specified separately as the corrosion allowance equivalent.

How Much Does Each Millimetre Cost?

Converting thickness into money makes the design decisions concrete. For a cylindrical shell, the mass per millimetre of wall is the wetted area times 1 mm times the density, and for a 3.0 m inside diameter, 6 m long shell the wetted area is π × 3.0 × 6 = 56.5 m².

Table 3 — Cost of wall thickness for a 3.0 m × 6 m shell

The pattern is linear and unremarkable: about USD 800 per millimetre per 6 m of shell at this diameter, or roughly USD 160 per millimetre per square metre of wetted area. Two consequences follow.

First, the radiography trade-off in Example 1 is easy to price: moving from E = 0.85 to E = 1.0 saved 3 mm, about USD 2,400 of plate on this shell, plus the weight and handling saving. Full radiography of the seams on a vessel this size typically costs more than that in direct NDE, so the case for full radiography rests on the downstream benefits — thinner plate procurement, less welding, lower weight, and a higher MAWP for the same thickness — rather than on NDE cost alone.

Second, at 4 m diameter and 76 mm wall the increments become large: each millimetre is about 0.6 t of steel on a 10 m shell, and the difference between a 76 mm and a 52 mm design is 14 t of plate and several days of welding. This is exactly the regime in which the code choice between Division 1 and Division 2 becomes a cost decision rather than a technical preference, as worked through in ASME VIII Div 1 vs Div 2.

Where Do These Calculations Go Wrong?

Seven errors account for most calculation-related problems we see in design reviews and in service.

1. Thickness is compliant on paper but the vessel is under-designed at the bottom. Symptom: measured thickness at the lower shell course is below the drawing value within a few years. Cause: design pressure omitted the static head, so the lower course should have been calculated at 1.68 MPa rather than 1.6 MPa. Correction: calculate the shell course by course using the pressure at the bottom of each course, or add the full static head to the design pressure for the whole shell.
2. A stainless vessel pits after hydrotest, before commissioning. Symptom: pitting clusters on the shell and in low points within weeks of the test. Cause: hydrotest water with chloride above the alloy’s tolerance, left standing. Correction: specify low-chloride test water, drain and dry immediately, and add a corrosion inhibitor where water must remain.
3. The head is thinner than the shell after forming. Symptom: ultrasonic readings at the head crown 1–2 mm below the shell. Cause: forming thinning not accounted for in the ordered plate. Correction: order head plate one increment thicker, or specify the minimum after forming and let the fabricator choose the starting thickness.
4. A nozzle requires a pad that the drawing does not show. Symptom: reinforcement calculations fail at the detailed design stage. Cause: UG-37 area replacement checked against nominal thickness without deducting corrosion allowance. Correction: run reinforcement on the corroded thickness, since the area available must exist at the end of life as well as at the start.
5. MAWP is quoted above the design pressure without justification. Symptom: nameplate and relief valve setting disagree. Cause: MAWP calculated on nominal thickness without deducting allowance, or with the wrong E. Correction: calculate MAWP on the thickness expected at the next inspection, and set the relief valve from the lower of MAWP and design pressure.
6. External pressure or vacuum cases are not checked at all. Symptom: shell deformation during steam-out or a vacuum upset. Cause: the design basis only covered internal pressure. Correction: run UG-28 for the vacuum case, add stiffening rings where the unstiffened span is too long, and state the vacuum condition on the drawing.
7. The wrong radius is used. Symptom: thickness systematically 1–3 mm low. Cause: outside radius substituted into an inside-radius formula, a common error when piping and vessel calculations are mixed in one spreadsheet. Correction: standardise the spreadsheet on inside dimensions and label every cell with its basis.

The last error is the most common, and it is worth a control: every thickness calculation sheet should state at the top whether dimensions are inside or outside, and the drawing should state the same thing in the same words. Most rework we see on vessel packages is not a metallurgical problem at all; it is a dimension convention problem.

Case Data: Three Vessels, Three Calculations

Case A — 2.4 m leach tank, E = 1.0, 18 mm. Design 1.6 MPa at 60 °C, SA-516-70, S = 138 MPa, R = 1,200 mm: t = 1,920/137.04 = 14.01 mm, plus 3 mm allowance = 17.01 mm, ordered 18 mm. Measured thickness after four years: 17.6 mm. Remaining life at the measured 0.1 mm/y rate: over 100 years against the 3 mm allowance, which confirms the vessel is allowance-rich and the inspection interval can be extended.

Case B — 3.0 m POX flash vessel, 30 mm. Design 3.5 MPa at 150 °C, SA-516-70, S = 132 MPa at temperature, R = 1,500 mm: t = 5,250/(132 − 2.1) = 40.4 mm, above the 38 mm PWHT trigger. The fabricator proposed reducing design pressure to 3.2 MPa, giving 36.9 mm, which crosses below the trigger and avoided a full furnace cycle worth USD 34,000. The engineering decision here was a pressure-rating decision, not a thickness decision.

Case C — 3.6 m autoclave, 50 mm, Division 2. Design 4.2 MPa at 210 °C, S = 183 MPa under Division 2, R = 1,800 mm: t = 7,560/(183 − 2.52) = 41.9 mm, plus 3 mm allowance = 44.9 mm, ordered 50 mm for corrosion and handling margin. The same duty under Division 1 at S = 125 MPa gives 61.7 mm plus allowance, ordered 65 mm — a 15 mm difference that on a 10 m shell is about 13 t of steel.

The three numbers to carry into a design basis are 14.01 mm calculated versus 18 mm ordered, the 38 mm PWHT trigger that converted a 40.4 mm design into a 36.9 mm one, and the 50 mm versus 65 mm spread between divisions at 4.2 MPa. All three are sensitive to the allowable stress read at temperature, so the design temperature assumption deserves the same review rigour as the pressure.

FAQ

Is the UG-27 formula valid for thick-walled vessels?
UG-27(c)(1) applies when the wall is thin relative to the radius, which Division 1 defines by a thickness limit relative to inside radius; beyond that limit UG-27(c)(2) applies, and for very thick sections Division 2 design-by-analysis is the appropriate route. A 76 mm wall on a 1.8 m radius is close enough to the limit that the formula choice should be checked explicitly.

Why is joint efficiency 0.85 sometimes used with full radiography?
It should not be. UW-12 assigns E by joint type and extent of examination; if full radiography is performed on a double-welded butt joint, E = 1.0. A 0.85 value with full RT usually indicates a Type 1 joint with spot RT, or a drawing carried over from another project without review.

Do I add corrosion allowance before or after rounding?
Add the allowance to the calculated pressure thickness first, then round the sum up to available plate. Rounding first and adding the allowance second can leave the vessel one plate increment thin, particularly where the calculation lands just below a standard size.

How do I calculate thickness for a vacuum vessel?
Use UG-28 for external pressure, which requires the geometry (outside diameter, thickness, unstiffened length), the material chart and a trial-and-error or chart-based solution. The result is an allowable external pressure for a given thickness, so the design is usually iterative; stiffening rings are often cheaper than wall thickness for large vessels.

What thickness do I use for the MAWP calculation after years in service?
The measured thickness at the next inspection interval, minus the corrosion allowance you intend to keep, or the measured thickness minus the minimum required — whichever is more conservative. The MAWP must be valid until the next inspection, not only on the day it is calculated.

Does Division 2 use the same formula?
Division 2 Part 4 provides an equivalent rule-based formula with a different allowable stress and mandatory E = 1.0, so the arithmetic looks similar but the answer differs by 25–35% at high pressure. Design-by-analysis under Part 5 is an alternative route, not the default.

Does a pressure vessel wall thickness calculation change for clad plate?
Yes, in one specific way: the pressure thickness is calculated on the base metal alone, and the clad or overlay layer is excluded from the calculation even though it appears on the drawing. The clad thickness is then specified separately as the corrosion allowance equivalent, usually 3 mm.

How much does 1 mm of wall cost on a large vessel?
At 4 m diameter and 10 m length, each millimetre is roughly 1.0 t of plate, so about USD 1,800 at indicative plate prices, plus welding time. At 3 m diameter and 6 m length it is about 0.44 t and USD 800.

Conclusion

Pressure vessel wall thickness calculation is simple arithmetic wrapped in four decisions: which allowable stress applies at design temperature, what joint efficiency the examination plan justifies, how much corrosion allowance the duty needs, and which plate thickness is actually available. Get those four right and UG-27 gives you a number you can defend.

If you are sizing a vessel for a leach, SX or evaporation duty and want the thickness, MAWP and hydrotest pressure checked against your design basis, send the process conditions through our turnkey plant engineering route. For the alloy decision upstream of the arithmetic, start with pressure vessel material selection.

References

1. ASME Boiler and Pressure Vessel Code, Section VIII, Division 1 — UG-16, UG-27, UG-28, UG-32, UG-37, UG-99, UW-12.
2. ASME Boiler and Pressure Vessel Code, Section II, Part D — Properties (Metric), Tables 1A and 1B.
3. ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 — Part 4 and Part 5.
4. SME Mineral Processing Handbook — vessel and tank design practice. smenet.org
5. MetSoc Conference of Metallurgists (COM) proceedings — autoclave and pressure vessel design papers.
6. USGS Mineral Commodity Summaries — copper, gold and nickel production context. usgs.gov
7. EN 13445 Unfired Pressure Vessels — European equivalent design rules for comparison.

Changelog

• 2026-10-17 — First publication. UG-27 and UG-32 worked examples, MAWP and hydrotest, thickness cost table, seven calculation errors.

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