Pressure Vessel Calculator — MAWP, Wall Thickness & Stress (ASME VIII Div.1)

Governing standard: ASME VIII Div.1· ASME Boiler & Pressure Vessel Code Section VIII Division 1 — UG-27 (cylinder), UG-32 (heads), UG-34 (flat heads), UG-37/UG-45 (nozzle), Mandatory Appendices 1-2 & 1-3 (thick-wall); ASME B16.5-2017 flange ratings

Page last updated 20 October 2026

How ASME VIII works — the method explained

Video walkthrough (3:19)

Read the transcript

Here's a steel pressure vessel, a 1 m drum at 1.6 MPa. The tool says it's SAFE, with a safety factor of 3.69.

Now raise the pressure to 4 MPa. Same vessel, and the verdict changes to CHECK.

This is the MechanixCalc pressure vessel calculator, to ASME Section VIII, Division 1. It sizes the shell and the heads, and works out the maximum allowable pressure. Let's go through it, step by step.

Pressure pushes outward on the wall. In a cylinder, the hoop stress around the circumference is twice the stress along its length.

So the shell is sized on the hoop stress, and every head shape has its own formula. A flat head needs far more wall than a curved one.

Step one is the design conditions. 1.6 MPa at 200 °C, with a 3 mm corrosion allowance. Every check runs on the corroded wall.

Step two is the material, carbon steel SA-516 Grade 70, with an allowable stress of 138 MPa.

The weld joint efficiency starts at 1.00, full radiography. The tool won't assume that, so the verdict reads CHECK until you confirm it.

Step three is the shell and the head. A 1000 mm bore, a 25 mm wall, and hemispherical heads.

Step four shows the checks. The hoop stress is 37.4 MPa against 138, a safety factor of 3.69.

The shell needs 8.88 mm and the head 5.92, both with the corrosion allowance, and the wall is far above the Code minimum. So the verdict is SAFE.

The vessel's maximum allowable pressure is 5.881 MPa, set by the shell.

Now raise the design pressure to 4 MPa. The hoop stress rises to 93.5 MPa, and the safety factor falls to 1.48.

That's still above 1, and the wall still clears the 17.84 mm Code minimum. But it's below the 1.5 design margin, so the verdict is CHECK.

The fix is a thicker wall. At 28 mm the safety factor is 1.67, and the verdict turns green.

Now try a flat head. It needs a 101.39 mm wall, and the vessel's allowable pressure drops to 0.258 MPa. The verdict is FAIL.

A flat plate carries the pressure in bending, not in tension, so it needs several times the wall of a curved head.

The fix is a 2:1 ellipsoidal head. It needs 17.63 mm, and the verdict turns green.

The head is held to the same 1.5 margin as the shell. This one has 1.71, so the shell still governs.

What the tool does not check is listed too: external pressure, supports and nozzle loads, and fatigue. So silence never reads as a pass.

Every input, every formula and every check goes into a PDF report. A report your reviewer can follow.

That's a pressure vessel, checked. Try it on your own design, on MechanixCalc.com.

The MechanixCalc pressure vessel calculator sizes and verifies cylindrical shells and heads to ASME Boiler & Pressure Vessel Code Section VIII Division 1. Enter the inner radius, wall thickness, design pressure, temperature, corrosion allowance and material, and the tool returns the minimum required wall thickness (UG-27), the maximum allowable working pressure (MAWP), the hoop and longitudinal stresses, the von Mises equivalent stress, and the ASME safety factor — with the hoop stress taken as the exact Lamé thick-wall value at the bore at every wall-to-radius ratio.

Subsidiary panels cover wall thickness design for three head types (ellipsoidal 2:1, hemispherical and flat; the main check also sizes the torispherical head), a nozzle reinforcement screening check with ASME B16.5 flange pressure-temperature ratings from −29 to 538 °C, and a combined creep utilisation / thermal fatigue life assessment. It is built for process, mechanical and chemical engineers who need a defensible, standards-cited calculation for vessels at the concept and detailed-design stage — and who need to hand a reviewer a worked number rather than a spreadsheet.

What this calculator does

ASME VIII Div.1 UG-27 minimum wall thickness and back-calculated MAWP for cylindrical shells, with automatic switchover to the Mandatory Appendix 1-2 thick-wall equation above 0.385·S·E
Lamé hoop and radial stress at every wall ratio (40-point through-wall profile with von Mises and maximum shear); longitudinal stress in the conservative membrane form below t/R = 0.10 and the exact closed-end value above
All four ASME head types: ellipsoidal 2:1 (UG-32d), hemispherical (UG-32f), torispherical with M-factor (UG-32e), and flat plate (UG-34) with attachment-factor selector
Nozzle reinforcement screening estimate (UG-45/UG-37 t_n_min) and ASME B16.5-2017 Class 150–2500 flange pressure ratings from −29 to 538 °C
Creep utilisation (σ_θ / σ_creep) vs temperature and Miner's-rule thermal fatigue damage for four materials (carbon steel, 304 SS, 316 SS, Cr-Mo steel)
Four built-in material allowables (SA-516-70, SS-304, SS-316L, Al-5083-O — the Al-5083 value is derived from the Code room-temperature criterion on ASTM B209 minimum properties for the O temper, not read from II-D, and this is stated in the results) plus a custom-allowable entry — each S is a single tabulated constant, NOT derated for temperature: above 300 °C for carbon steel (40 °C for the stainless and aluminium entries) the verdict reads CHECK until a temperature-derated allowable from ASME Sec. II-D is entered, and an unconfirmed full-RT joint efficiency (1.00) reads CHECK too
Branded PDF engineering report with the full ASME method, substituted formulas and pass/warn/fail verdict shown

Method & formulas

Minimum wall thickness and MAWP (ASME VIII Div.1 UG-27)

ASME UG-27(c)(1) gives the minimum net wall thickness for a cylindrical shell under internal pressure. The formula is valid while t ≤ R/2 (i.e. P ≤ 0.385·S·E); above that limit MechanixCalc automatically uses the Mandatory Appendix 1-2 thick-wall equation, which replaces the linear approximation with the exact Lamé bore-hoop-stress criterion. The corrosion allowance CA is added to the net thickness to get the required nominal wall t_req. MAWP is the inverse of the same equations evaluated at the net (corroded) thickness.

Required cylinder wall — ASME UG-27(c)(1)

t_min = P · R / (S · E_j − 0.6 · P) (valid for P ≤ 0.385 · S · E_j)

where t_min = minimum net wall thickness (mm); P = design pressure (MPa); R = corroded inner radius (mm); S = allowable stress at design temperature (MPa); E_j = weld joint efficiency (0.70 / 0.85 / 1.00)

MAWP back-calculation (UG-27 inverse)

MAWP = S · E_j · t_net / (R + 0.6 · t_net)

where t_net = nominal wall − CA (mm); R = corroded inner radius (mm); S · E_j = effective allowable stress (MPa)

Thick-wall Lamé stress distribution

As the wall thickens the membrane assumption stops holding, and the membrane formula under-reads the bore stress (by about 5 % already at t/R = 0.10). MechanixCalc therefore uses the full Lamé equations at every wall ratio: it evaluates the circumferential (hoop) and radial stresses at every radial position from the bore to the outer surface, and combines them with the closed-end longitudinal stress to give the von Mises equivalent stress and the maximum shear stress. The highest hoop stress always occurs at the inner bore, making it the critical location for the ASME allowable check.

Lamé hoop stress (circumferential, at radius r)

σ_θ(r) = P · r_i² / (r_o² − r_i²) · (1 + r_o² / r²)

where r_i = corroded inner radius (mm); r_o = outer radius (mm); r = radius at the evaluation point (mm); P = design pressure (MPa). Maximum occurs at r = r_i (the bore).

Head design and nozzle reinforcement

Each head type is sized to its own ASME clause: the ellipsoidal 2:1 head uses UG-32(d) with the inner diameter; the hemispherical head uses UG-32(f), branching to the Appendix 1-3 thick-sphere equation above 0.665·S·E; the torispherical head uses UG-32(e) with the Appendix 1-4(d) M-factor; and the flat head uses UG-34(c)(2) with the attachment-factor C from Figure UG-34. The nozzle panel estimates reinforcement adequacy per the UG-45 minimum nozzle-wall criterion and credits the nozzle-wall excess area against the required reinforcement area; this is a conservative screening check, not a full UG-37 area-replacement calculation (the in-app warning makes this explicit).

Torispherical head M-factor — ASME Appendix 1-4(d)

M = (3 + √(R_crown / r_knuckle)) / 4

where R_crown = crown radius (mm); r_knuckle = knuckle radius (mm). M increases wall thickness requirements for flatter heads.

Worked example

Size the minimum wall thickness and determine the MAWP for a thin-wall cylindrical pressure vessel with a 500 mm inner radius, carrying a design pressure of 1.5 MPa. Material: SA-516-70 carbon steel (S = 138 MPa), full-radiography weld (E_j = 1.00), corrosion allowance CA = 1.5 mm.

Given

Inner radius R (corroded: R + CA)500 + 1.5 = 501.5 mm
Design pressure P1.5 MPa
Allowable stress S138 MPa (SA-516-70)
Weld joint efficiency E_j1.00 (full RT)
Corrosion allowance CA1.5 mm

Result

Minimum required wall t_req (net + CA)≈ 6.99 mm → use 8 mm nominal
MAWP (at 8 mm nominal, corroded)≈ 1.775 MPa
Hoop stress at P = 1.5 MPa (Lamé)≈ 116.5 MPa (SF 1.18 → CHECK; 10 mm → SF 1.55, SAFE)

Check thin-wall validity: t/R is small (t << R = 500 mm), so UG-27(c)(1) applies (we verify t ≤ R/2 after computing t).
Compute minimum net thickness using UG-27(c)(1): t_min = P · R_corr / (S · E_j − 0.6 · P) = 1.5 × 501.5 / (138 × 1.00 − 0.6 × 1.5) = 752.25 / (138 − 0.9) = 752.25 / 137.1 ≈ 5.49 mm.
Add corrosion allowance: t_req = 5.49 + 1.5 = 6.99 mm. Round up to the next standard plate: 8 mm nominal.
Check thin-wall validity: t = 8 mm, R = 500 mm → t/R = 0.016 << 0.10. Thin-wall confirmed.
Compute net thickness for MAWP back-calc: t_net = 8 − 1.5 = 6.5 mm.
MAWP = S · E_j · t_net / (R + 0.6 · t_net) = 138 × 1.00 × 6.5 / (501.5 + 0.6 × 6.5) = 897 / (501.5 + 3.9) = 897 / 505.4 ≈ 1.775 MPa.
Hoop stress at design pressure (Lamé at the bore, as the tool reports it; corroded bore a = 501.5, outside b = 508): σ_θ = P · (a² + b²) / (b² − a²) = 1.5 × 509 566 / 6 562 ≈ 116.5 MPa (the thin-wall P · R / t_net gives 115.7).
Safety factor: SF = S · E_j / σ_θ = 138 / 116.5 ≈ 1.18 — above 1, so the 8 mm plate holds at design pressure, but below the 1.5 target, so the tool reads CHECK. A 10 mm plate (t_net = 8.5 mm, b = 510) gives σ_θ ≈ 89.3 MPa and SF ≈ 1.55 ≥ 1.5 — SAFE.

Illustrative only — verify with your actual material specification, corrosion allowance, and head/nozzle geometry. A code-stamped vessel requires a full UG-37 nozzle check, head calculations, and a registered inspector.

Frequently asked questions

Which standard does this pressure vessel calculator use?

The main cylinder and head calculations follow ASME Boiler & Pressure Vessel Code Section VIII Division 1 (ASME VIII Div.1): UG-27(c)(1) for cylinder wall thickness and MAWP, UG-32 for ellipsoidal, hemispherical and torispherical heads, UG-34 for flat heads, and Mandatory Appendix 1-2/1-3 for thick-wall regimes. Flange ratings follow the ASME B16.5 pressure-temperature ratings for Material Group 1.1. The governing clause is shown in the generated PDF report. The creep/thermal-fatigue sub-panel is an engineering estimate (flagged in-app) with no governing standard.

When does the calculator switch from thin-wall to thick-wall (Lamé)?

There are two separate switches, and they are not the same condition. The THICKNESS and MAWP clauses follow the Code's own validity limit: UG-27(c)(1) applies while t ≤ R/2, i.e. P ≤ 0.385·S·E_j, and above it MechanixCalc uses the Mandatory Appendix 1-2 equation. The reported HOOP STRESS does not switch at all: it is the exact Lamé bore value at every t/R, which is never below the thin-wall membrane value. Only the reported LONGITUDINAL stress changes form, at t/R ≥ 0.10, from the conservative membrane value to the exact closed-end Lamé value, and the tool shows which form it used.

Does it cover different head types?

Yes — all four ASME head types are included. Ellipsoidal 2:1 heads use UG-32(d) with the inner diameter. Hemispherical heads use UG-32(f) with the thick-sphere Appendix 1-3 branch above 0.665·S·E. Torispherical heads use UG-32(e) with the computed M-factor (crown/knuckle ratio). Flat heads use UG-34(c)(2) with a selectable attachment-factor C from Figure UG-34, defaulting to the conservative welded value of 0.33. Each head's MAWP is also back-calculated from the actual wall thickness.

What does the nozzle reinforcement panel compute?

The nozzle panel is a screening estimate, not a full ASME UG-37 area-replacement calculation. It sizes the minimum nozzle wall (UG-45) and credits only the nozzle-wall excess area against the required reinforcement area, omitting the dominant shell-credit term A1 and the weld-area contributions. For valid designs this is conservative, but a code-stamped vessel always requires the complete UG-37 calculation. The flange-rating check covers ASME B16.5 Class 150 through 2500, Material Group 1.1 (carbon steel), from −29 to 538 °C; verify the rating against the current edition for your flange material.

Is the pressure vessel calculator free?

You can run it during a free 30-minute preview with no sign-up required, and a free 14-day account trial unlocks every calculator with no credit card needed. The branded PDF engineering report with the full ASME method shown and saved calculations are included in the free 14-day trial and in every paid plan.

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