Hemispherical Dish End Weight Calculator – Quick & Accurate | WeldFabWorld

Hemispherical Dish End Weight Calculator — Quick & Accurate

📅 April 7, 2022 · Updated Sep 3, 2025 ⏱ 10 min read ✍️ WeldFabWorld 🏷️ Fabrication & Calculators

Hemispherical dish ends are a fundamental component of pressure vessels, storage tanks, and process equipment across oil & gas, petrochemical, power generation, and pharmaceutical industries. Accurately calculating their weight is essential for structural support design, material procurement, crane lift planning, and freight cost estimation. This page provides a fully plugin-free, instant dish end weight calculator supporting hemispherical, semi-ellipsoidal, and torispherical heads — complete with skirt height, multiple materials, and a full step-by-step formula breakdown.

🔵 Dish End Weight Calculator

Hemispherical · Semi-Ellipsoidal (2:1) · Torispherical (Klöpper/Korbbogen) · with optional skirt

Inside Diameter (ID)

Diameter Unit

Wall Thickness (T)

Thickness Unit

Quantity (no. of heads)

Material

Include straight skirt / flange flange height

—Per head (kg)

—Total (kg)

—Total (lb)

A hemispherical dished end (also called a hemispherical head or hemispherical cap) is a dome-shaped end closure formed as an exact half-sphere. Its geometry gives it the highest structural efficiency of all head types — it can withstand twice the internal pressure of a cylindrical shell of the same diameter and thickness, and its stress distribution is perfectly uniform. This makes it the preferred choice for high-pressure vessels and reactors in demanding industrial service.

Understanding how dish end weight is calculated — and why different head types have different weights for the same diameter — helps engineers make informed decisions about material selection, fabrication methods, and pressure vessel design optimisation from the earliest project stage.

Types of Pressure Vessel Dish Ends

Pressure vessels use several standard head geometries, each offering a different balance of structural efficiency, fabrication cost, height, and internal volume. The four most common types are compared below:

Fig 1 — Comparison of the four main pressure vessel head types: hemispherical, semi-ellipsoidal (2:1), torispherical (Klöpper), and flat. Height (H) relative to inside diameter (D) shown for each.

Head Type	Height (H)	Depth Ratio	Typical T vs Shell	Relative Weight	Pressure Rating	Best For
Hemispherical	H = D/2 (= R)	1 : 2	~T_shell / 2	Medium	Highest	High-pressure reactors, boilers
Semi-Ellipsoidal (2:1)	H = D/4	1 : 4	= T_shell	Medium	High	General ASME vessels, most common
Torispherical (Klöpper)	H ≈ 0.19 × D	1 : 5.3	= T_shell	Lightest	Moderate	Low to medium pressure, cost-driven
Flat End	H = T only	—	3–4 × T_shell	Heaviest	Low	Atmospheric tanks, low-pressure covers

The Hemispherical Dish End Weight Formula

The weight of a hemispherical dish end is calculated from its surface area multiplied by its wall thickness (giving volume) and then by the material density. Because a hemisphere is exactly half a sphere, its curved surface area is 2πR², where R is the mid-surface radius of the head.

Key Dimensions OD = ID + 2T (Outside Diameter of head)
R_mid = (ID + T) / 2 (Mid-surface radius)

Curved Surface Area of Hemisphere A_curved = 2 × π × R_mid²

Volume of Curved Shell V_curved = A_curved × T = 2π × R_mid² × T

Add Skirt (straight cylindrical flange, height h) V_skirt = π × R_mid × 2 × h × T (cylindrical ring)

Total Weight per Head W = (V_curved + V_skirt) × ρ

Where: T = wall thickness · ρ = material density · R_mid = (ID/2) + (T/2)

Semi-Ellipsoidal (2:1) Head Formula

The standard 2:1 semi-ellipsoidal head (the most common ASME head type, with height equal to one-quarter of the inside diameter) has an outer curved surface area approximated as:

Semi-Ellipsoidal (2:1) — Curved Surface Area A = π × a × b / e × arcsin(e)
where a = semi-major axis = R_mid, b = semi-minor axis = R_mid/2, e = eccentricity

Simplified practical formula (industry standard approximation) A_ellip ≈ 2 × π × (R_mid² + h²/2) [for 2:1 where h = R_mid/2]
This simplifies for a 2:1 head to approximately: A ≈ 2π × R_mid² × 0.875

Torispherical (Klöpper) Head Formula

The Klöpper head (the standard European torispherical form per DIN 28011) has a crown radius equal to the inside diameter and a knuckle radius of 10% of the inside diameter. Its surface area is approximated as:

Torispherical (Klöpper / DIN 28011) — Surface Area Approximation A_tori ≈ 2 × π × R_mid² × 0.655
This is a practical approximation; the exact value requires numerical integration of the toroidal and spherical zones separately.

Fig 2 — Hemispherical dish end cross-section showing inside diameter (ID), wall thickness (T), head height (H = ID/2), mid-surface radius (R_mid), and optional skirt height (h).

Worked Calculation Example

Let’s calculate the weight of a pair of hemispherical heads for a carbon steel pressure vessel with ID = 1,200 mm and wall thickness T = 14 mm, including a 50 mm straight skirt on each head:

Given Data ID = 1,200 mm · T = 14 mm · Skirt height h = 50 mm · Material: Carbon Steel (ρ = 7,850 kg/m³) · Qty: 2 heads

Step 1 — Mid-surface radius R_mid = (1200 + 14) / 2 = 607 mm = 0.607 m
Step 2 — Curved surface area (hemisphere) A = 2 × π × 0.607² = 2 × 3.14159 × 0.3685 = 2.317 m²
Step 3 — Volume of curved dome shell V_dome = A × T = 2.317 × 0.014 = 0.03244 m³
Step 4 — Skirt volume (cylindrical ring) V_skirt = π × (ID + T) × T × h = π × 1.214 × 0.014 × 0.050 = 0.002670 m³
Step 5 — Total volume per head V_total = 0.03244 + 0.002670 = 0.03511 m³
Step 6 — Weight per head W_single = 0.03511 × 7850 = 275.6 kg
Step 7 — Total for 2 heads W_total = 275.6 × 2 = 551.2 kg

Why Hemispherical Heads Are Preferred for High-Pressure Applications

The hemispherical head’s geometric advantage stems from the way it distributes stress. In a cylindrical pressure vessel, the hoop (circumferential) stress in the shell wall is:

σ_hoop (cylinder) = P × R / T

For a hemispherical head of the same radius R, the stress is only:

σ_meridional = σ_circumferential = P × R / (2T)

This means a hemispherical head at the same pressure and radius only needs half the wall thickness of the cylindrical shell to achieve the same stress level. In practice, this is why ASME Section VIII Div. 1 (UG-32) allows hemispherical heads to have thinner walls than the connecting shell — the head’s strength advantage partially offsets the material cost of forming the complex curved shape.

Code Reference (ASME Section VIII Div. 1, UG-32): For hemispherical heads under internal pressure, the required thickness is approximately half that of a cylindrical shell of the same inside radius and pressure rating. This is why hemispherical heads are specified for reactors, autoclaves, and high-pressure vessels despite their higher fabrication cost compared to ellipsoidal or torispherical heads.

Fabrication Methods for Hemispherical Dish Ends

Hemispherical heads can be manufactured by several methods depending on the diameter, wall thickness, material, and available equipment. Each method produces a different surface quality, dimensional tolerance, and wall thickness distribution:

Spinning (Rotary Forming)

Spinning is the most economical method for smaller diameters (typically up to ~1,500 mm). A flat circular blank (cut from plate) is rotated at high speed and progressively worked against a mandrel by a series of forming rollers. The process thins the material slightly from the original blank thickness, so the blank must be cut slightly thicker than the required finished thickness. Spinning produces excellent surface finish and tight dimensional tolerances.

Pressing (Stamping)

For larger diameters or thicker walls, pressing between male and female dies is the standard method. The blank is placed between the dies and pressed in a single or multi-stage operation. Large hydraulic presses can form heads up to 5,000 mm diameter from heavy plate. Multiple pressing stages are required for thick-walled or small-radius heads to avoid wrinkling or tearing. The head is typically re-heated between stages to restore material ductility for alloy steels and stainless steels.

Segmental Construction (Petalling)

Very large diameter heads (above ~3,000–4,000 mm for most fabricators) are constructed from petal-shaped segments cut from plate, formed individually, and welded together to form the complete hemisphere. This method allows heads of virtually unlimited size to be fabricated in workshops with limited press capacity. The welds between segments are Category A joints per ASME Section VIII and must be fully radiographed in most applications. Careful fit-up and welding sequence control are critical to maintain the correct profile and minimise distortion.

Fabrication Tolerance Note: After forming, all pressure vessel heads must be inspected for dimensional conformance. Per ASME Section VIII Div. 1 (UG-81), the finished head must conform to its specified shape within a tolerance of ±1.25% of the inside diameter measured along the inner surface. Out-of-tolerance heads can introduce bending stresses not accounted for in the design pressure calculation.

Common Materials & Densities for Dish End Calculations

The choice of material for pressure vessel heads is governed by the operating temperature, process fluid chemistry, pressure rating, and applicable design code. The table below provides the density values used in this calculator and their typical applications in pressure vessel fabrication:

Material	Density (kg/m³)	Common ASTM Grade	Typical Vessel Application
Carbon Steel	7,850	SA-516 Gr.60/70, SA-537	General storage, low-temp service
Alloy Steel (Cr-Mo)	7,750	SA-387 Gr.11/22/P91	High-temp pressure vessels, boilers
Stainless Steel 304/316	7,980	SA-240 TP304L/316L	Corrosive service, food, pharma
Stainless Steel 321/347	7,900	SA-240 TP321/347	High-temp stainless, sensitisation resistance
Duplex Stainless	7,800–8,400	SA-240 UNS S31803/S32205	Offshore, sour service, seawater
Nickel Alloy (Inconel)	8,900	SB-443 UNS N06625	High-temp / highly corrosive environments
Titanium	4,500	SB-265 Gr.1/2	Highly corrosive acid service, marine
Aluminium	2,700	SB-209 Gr.5052/5083	Cryogenic service, lightweight vessels
Copper	8,960	SB-11, SB-169	Heat exchangers, brewing, food processing

Frequently Asked Questions

What is a hemispherical dished end used for?

Hemispherical dished ends are used as end closures on pressure vessels, storage tanks, reactors, and autoclaves. Their dome shape distributes internal pressure as uniform membrane stress across the curved surface — with no bending stresses — making them structurally the most efficient head type. They are specified for high-pressure applications such as chemical reactors, pressure vessels in oil & gas processing, and power generation boilers where the additional forming cost is justified by reduced wall thickness and long service life.

What is the formula for hemispherical dish end weight?

The weight per head = 2π × R_mid² × T × ρ, where R_mid = (ID + T)/2 is the mid-surface radius, T is the wall thickness, and ρ is the material density. If a straight skirt (cylindrical flange) is included, add the skirt volume: π × (2 × R_mid) × T × h, where h is the skirt height. The calculator on this page performs this calculation automatically with unit conversion and displays a step-by-step breakdown.

What is the difference between a hemispherical and a semi-ellipsoidal head?

A hemispherical head is a true half-sphere with height H = ID/2. A semi-ellipsoidal head (the standard 2:1 type per ASME Section VIII) has height H = ID/4 — meaning it is shallower and requires less axial space. The hemispherical head has 30–40% lower stress for the same pressure and can use approximately half the wall thickness of the shell, while the semi-ellipsoidal head requires the same wall thickness as the connecting shell. The semi-ellipsoidal head is considerably cheaper to fabricate but requires more material thickness.

Why does the ASME code allow a thinner hemispherical head than the shell?

Per ASME Section VIII Div. 1 (UG-32d), the hoop and meridional stresses in a hemispherical head under internal pressure are both equal to P×R/(2T) — exactly half the hoop stress in a cylindrical shell at the same radius (P×R/T). This means the head only needs half the wall thickness of the cylindrical shell to maintain the same stress margin. This is why ASME allows the hemispherical head thickness to be as little as T_shell/2, making it the only head type where the head can legally be thinner than the shell.

Does the calculator include the weight of the straight skirt (flange)?

Yes — enable the “Include straight skirt” toggle and enter the skirt height. The skirt (also called the straight face or straight flange) is the short cylindrical section at the base of the dome that allows the head to be welded onto the shell with a standard Category A circumferential butt weld. Most pressure vessel heads are supplied with a standard 25–50 mm skirt as part of the formed head assembly. The calculator treats the skirt as a thin cylindrical ring and adds its weight to the dome weight.

How is dish end weight relevant to pressure vessel procurement?

Dish end suppliers typically quote prices on a per-kilogram basis (with a forming premium). Accurate weight calculation allows project engineers to estimate material cost, compare quotes from multiple suppliers, verify mill certificates, and generate the material take-off (MTO) for overall project budgeting. The pair of heads on a typical pressure vessel can represent 15–30% of the total vessel shell and head material weight, making accurate head weight calculation significant for procurement accuracy.

What is a torispherical head and how does it differ from a hemispherical head?

A torispherical head consists of a central spherical zone (crown radius) and a toroidal zone (knuckle radius) connecting the crown to the straight cylindrical skirt. The Klöpper form (DIN 28011) has crown radius = ID and knuckle radius = 0.1 × ID. The Korbbogen (basket handle) form has crown radius = 0.8 × ID and knuckle radius = 0.154 × ID. Torispherical heads are shallower (H ≈ 0.19 × ID for Klöpper) and cheaper to fabricate than hemispherical heads, but have lower pressure efficiency and require the same wall thickness as the shell. They are the most economical choice for low-to-medium pressure vessels.

What is the significance of the skirt height in dish end weight estimation?

The straight skirt (straight face) is the cylindrical extension at the open end of the head that allows the head to be positioned and welded onto the vessel shell. Standard skirt heights range from 25 mm (small vessels) to 100 mm (large vessels). The skirt weight can be 5–15% of the dome weight for thin-walled heads on large vessels, so it should always be included in accurate weight calculations. The skirt also provides the accessible weld prep location for the Category B head-to-shell circumferential joint.