Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Calculate minimum head thickness per ASME Section VIII Division 1 for semi-ellipsoidal, torispherical, and hemispherical heads. Input design pressure, allowable stress, internal diameter, and corrosion allowance.
What this calculator is used for
This calculator estimates the minimum required thickness for pressure vessel heads
under internal pressure. Unlike cylindrical shells, vessel heads have complex stress
distributions due to their curved geometry, making proper thickness design essential
for safe pressure containment.
Typical engineering use cases
Preliminary mechanical design of pressure vessels
Comparison of different head geometries for cost and weight optimization
Supporting ASME and JIS code-compliant calculations
Initial manufacturability and cost assessments
Material specification for fabrication procurement
Governing equation and methodology
Different formulas apply depending on head geometry:
Hemispherical heads: Thinnest but highest fabrication cost
2:1 Semi-ellipsoidal heads: Common balance of strength and manufacturability
Torispherical (dish-shaped) heads: Economical for low-pressure applications
These equations are derived from classical shell theory and align with ASME Section VIII
and equivalent international standards.
Engineering assumptions and limitations
Internal pressure loading only
External loads and nozzle reinforcement not considered
Uniform material properties assumed
Weld joint efficiency applied as specified
Practical design notes
Hemispherical heads require the thinnest material but are typically more expensive to
fabricate. Semi-ellipsoidal heads are commonly selected as a balance between strength
and manufacturability. Final thickness must include corrosion allowance and fabrication
tolerances. Always verify designs against the applicable pressure vessel code.
Worked Example
Given:
2:1 semi-ellipsoidal head, internal pressure P = 1.0 MPa
Inside diameter D = 2000 mm
Allowable stress S = 138 MPa, joint efficiency E = 1.0
Method: Using the 2:1 ellipsoidal-head internal-pressure relation represented by this calculator: t = P·D/(2·S·E − 0.2·P) = 1.0·2000/(2·138·1.0 − 0.2·1.0).
Result: t ≈ 7.3 mm minimum (before corrosion allowance).
Interpretation: Note the head comes out thinner than the matching shell (≈ 8.6 mm for the same duty) — that is why 2:1 ellipsoidal heads are the default. A hemispherical head would be thinner still but costs more to form, so this geometry is the usual cost/weight optimum; add CA and round to plate gauge.
Common Mistakes & Misuse
Carrying the cylindrical shell formula straight onto the head — each head type (2:1 ellipsoidal, torispherical, hemispherical) has its own stress factor and thickness.
Ignoring the knuckle/crown geometry of a torispherical head, where the high stress at the knuckle, not the crown, often governs.
Designing for internal pressure only and missing the separate external-pressure (vacuum) buckling check.
Taking the calculated minimum as the order thickness without adding corrosion allowance and forming thinning at the knuckle.
Frequently Asked Questions
Which head type is most efficient for pressure containment?
Hemispherical heads are most efficient (thinnest for same pressure), followed by semi-ellipsoidal (2:1), then torispherical. However, hemispherical heads are more expensive to fabricate, so 2:1 ellipsoidal is the most common choice.
Does this apply to external pressure?
This calculator covers internal pressure design only. External pressure (vacuum) design requires a different calculation considering buckling, per ASME Section VIII Division 1.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.