Why does a torispherical head need more thickness than a 2:1 ellipsoidal head?

For the same P, D, S, and E, UG-32(e) with L = D applies the 0.885 crown factor and yields a larger t_req than UG-32(d). A hemispherical head (UG-32(f)) is typically the thinnest.

Can I use this calculator for vacuum or jacket external pressure?

No. This tool covers internal pressure on the concave side only. External pressure and vacuum are governed by UG-28 charts and rules.

What corrosion allowance should I enter?

Use the project vessel specification. Typical carbon-steel process vessels use 1.5–3.0 mm; stainless often uses 0 mm when corrosion is negligible. The calculator adds C.A. after UG-32: t_nom = t_req + C.A.

Pressure Vessel Head Thickness (ASME VIII-1 UG-32) — Torispherical · ID 2000 mm · 2.0 MPa

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

ASME BPVC Section VIII Division 1 UG-32 · ASME BPVC Section VIII Division 1 Mandatory Appendix 1 · ASME BPVC Section II Part D Table 1A

t_req = P · D2 S E − 0.2 P (2:1 ellipsoidal · UG-32(d))

t_req = 0.885 P · LS E − 0.1 P (torispherical · L = D · UG-32(e))

t_req = P · R2 S E − 0.2 P (hemispherical · R = 0.5 D · UG-32(f))

t_req = P · D2 cos(α) (S E − 0.6 P) (conical · α ≤ 30° · UG-32(g))

t_nom = t_req + C.A.

2:1 Ellipsoidal UG-32(d)Torispherical L=D UG-32(e)Hemispherical UG-32(f)Conical α≤30° UG-32(g)

ASME Section VIII Division 1 Paragraph UG-32 sizes formed heads for internal pressure on the concave side. Symbols use t_req for the pressure-resisting minimum and t_nom = t_req + corrosion allowance for nominal design thickness — distinct from B31.3 pipe t_nom_req (mill under-tolerance). Confirm allowable stress S from the project edition of Section II Part D Table 1A.

t_req (Minimum required thickness) — Pressure-resisting head thickness from UG-32 before corrosion allowance (mm or in).
t_nom (Nominal design thickness) — t_nom = t_req + C.A. — ordered plate / formed-head design thickness screen.
P (Internal design pressure) — Internal design gauge pressure (MPa or psi).
D (Inside diameter) — Head inside diameter at the skirt / attachment plane (mm or in).
L (Inside crown radius) — Torispherical crown radius. This calculator uses L = D for standard 6% knuckle F&D screening.
R (Inside radius) — Hemispherical inside radius R = 0.5 D.
α (Half-apex angle) — Conical half-apex angle (degrees). UG-32(g) without knuckle limited to α ≤ 30°.
S (Allowable stress) — Maximum allowable tensile stress from ASME Section II Part D Table 1A at design metal temperature (MPa or psi).
E (Joint efficiency) — Weld joint efficiency (0.70 / 0.85 / 1.00) per radiography extent.
C.A. (Corrosion allowance) — Specified corrosion / erosion allowance added to t_req (mm or in).

2. Design Allowances & UG-32 Scope

Default screening duty is Metric 2:1 semi-ellipsoidal, ID 1500 mm, P 1.5 MPa, T 150 °C, SA-516 Gr.70, E = 1.00, C.A. = 3.0 mm. Results size concave-side internal pressure only.

Corrosion allowance (C.A.)0–12.5 mm / 0–0.5 in

Added after UG-32 pressure thickness: t_nom = t_req + C.A. Typical carbon-steel PV service uses 1.5–3.0 mm.

Joint efficiency (E)0.70 / 0.85 / 1.00

Radiography category per Section VIII joint type. Full radiography uses E = 1.00; spot radiography often E = 0.85.

Torispherical crown radiusL = D

Standard ASME flanged-and-dished (≈6% knuckle) screening sets inside crown radius L equal to inside diameter D.

Out of scopeUG-22 / UG-28 / nozzles

Wind, seismic, and nozzle local loads (UG-22), external pressure / vacuum (UG-28), and forming thinning / mill under-tolerance are not included. Complete a stamped vessel calculation package for fabrication.

Quick Reference Lookup Table

UG-32(d) 2:1 ellipsoidal head thickness at P = 1.5 MPa, T = 150 °C, SA-516 Gr.70 (S ≈ 137.9 MPa), E = 1.00, C.A. = 3.0 mm
Inside D (mm)	S (MPa)	t_req (mm)	t_nom (mm)
1000	137.9	5.44	8.44
1500	137.9	8.17	11.17
2000	137.9	10.89	13.89
2500	137.9	13.61	16.61
3000	137.9	16.33	19.33

At the same P/D/S/E/C.A. duty (ID 1500 mm), engine screens give torispherical t_nom ≈ 17.46 mm, hemispherical ≈ 7.08 mm, and conical (α = 30°) ≈ 12.48 mm — torispherical is thicker than 2:1 SE; hemispherical is thinnest.

3. Material Specifications & Temperature Limits

Allowable stress S is interpolated from ASME Section II Part D Table 1A screening curves bound in this calculator. Confirm the project code edition before stamped design.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
SA-516 Gr.70 (Carbon Steel Plate)	−29 °C to 482 °C (−20 °F to 900 °F) screening	20.0 ksi (137.9 MPa) through ≈400 °F; derates above 500 °F	Primary PV carbon plate. Long-term graphitization risk rises above ≈427 °C — follow project metallurgy limits.
SA-240 304L (Austenitic SS)	Cryogenic to ≈816 °C (1500 °F) stress table screen	16.7 ksi (115 MPa) near ambient; derates with temperature	Low-carbon austenitic plate for corrosive / clean services.
SA-240 316L (Austenitic SS)	Cryogenic to ≈816 °C (1500 °F) stress table screen	16.7 ksi (115 MPa) near ambient; Mo grade for chloride service	Molybdenum addition improves pitting resistance versus 304L.
SA-387 Gr.11 Cl.2 (1¼Cr–½Mo)	Up to ≈593 °C (1100 °F) screening	17.1 ksi (≈118 MPa) through mid-range temperatures	Cr-Mo alloy plate for elevated-temperature hydrocarbon services.

Code Applicability & Safety Boundaries

UG-32 formulas apply to internal pressure on the concave side only. External pressure / vacuum requires UG-28.
Conical heads without a knuckle are limited to half-apex angle α ≤ 30° under UG-32(g) as implemented here.
P/(S·E) > 0.385 triggers a thin-wall applicability REVIEW flag — confirm Appendix-1 / thick-wall rules for that duty.

4. Step-by-Step Worked Example

Field VerificationShow

Step-by-Step Worked Example: 2:1 Semi-Ellipsoidal Head

Size the required and nominal thickness for a 2:1 semi-ellipsoidal pressure vessel head at 1.5 MPa and 150 °C using SA-516 Gr.70 plate with full radiography and 3.0 mm corrosion allowance.

Head type:2:1 Semi-Ellipsoidal (UG-32(d))Inside diameter (D):1500 mmDesign pressure (P):1.5 MPaDesign temperature (T):150 °CMaterial:SA-516 Gr.70Allowable stress (S):137.9 MPa (20.0 ksi II-D screen)Joint efficiency (E):1.00 (full radiography)Corrosion allowance (C.A.):3.0 mm

Resolve allowable stress S at design temperature

T = 150 °C ≈ 302 °F. SA-516 Gr.70 II-D Table 1A screen remains 20.0 ksi through 400 °F → S = 137.9 MPa.

Result:S = 137.9 MPa

Apply UG-32(d) for 2:1 ellipsoidal head

Formula: t_req = P·D / (2·S·E − 0.2·P)

t_req = 1.5 × 1500 / (2 × 137.9 × 1.00 − 0.2 × 1.5) = 2250 / (275.8 − 0.3) = 2250 / 275.5

Result:t_req = 8.17 mm

Add corrosion allowance for nominal design thickness

Formula: t_nom = t_req + C.A.

t_nom = 8.17 mm + 3.00 mm

Result:t_nom = 11.17 mm

Back-calculate MAWP from t_req

Formula: P_MAWP = 2·S·E·t / (D + 0.2·t)

Using t = t_req = 8.17 mm returns MAWP ≈ 1.50 MPa, matching the design pressure for this screen.

Result:MAWP ≈ 1.50 MPa

Conclusion: Order / design around t_nom = 11.17 mm (t_req = 8.17 mm + 3.0 mm C.A.) for this Metric 2:1 SE duty. Confirm forming thinning, mill under-tolerance, and UG-22/UG-28 cases in the stamped calculation.

5. How to calculate ASME VIII-1 UG-32 head thickness

1
Select head geometry
Choose 2:1 ellipsoidal, torispherical (L = D), hemispherical, or conical (α ≤ 30°) to match the vessel drawing.
2
Enter D, P, T, material, E, and C.A.
Use inside diameter and internal design pressure. Material sets S(T) from the II-D screening curve; radiography sets E.
3
Read t_nom and t_req
Hero value is t_nom (with C.A.). Badge shows t_req without C.A. Review MAWP and UG-32 Pass/Fail status.
4
Export and carry related tools
Export JSON/CSV/PDF, then open Pipe Wall Thickness or Tank & Vessel Volume with the same D / P / T duty.

6. Frequently Asked Questions & Technical References

Show

No. UG-32 sizes formed pressure vessel heads. ASME B31.3 Para. 304.1.2 sizes straight pipe and uses different symbols (including mill under-tolerance t_nom_req). Do not interchange the formulas.