Pressure Vessel Torispherical Head Wall and Pressure Calculator

Pressure Vessel Design and Calculators

Torispherical head: These heads have a dish with a fixed radius (r1), the size of which depends on the type of torispherical head. The transition between the cylinder and the dish is called the knuckle. The knuckle has a toroidal shape.

Note: The inside crown radius to which an unstayed formed head is dished shall be not greater than the outside diameter of the skirt of the head. The inside knuckle radius of a torispherical head shall be not less than 6% of the outside diameter of the skirt of the head but in no case less than three times the head thickness.

Torispherical Heads. The required thickness and the design pressure of a torispherical head is calculated by the following formulas:

The following equations apply:

Torispherical Head Wall

Wall Thickness

Equation Torispherical Head Wall




 L [in] - inside diameter
   tn [in] - wall thickness before forming operations
 t [in] - thickness after forming 
 S [psi] - allowable stress 
 E - head efficiency 
 P [psi] - interior pressure
Calculated Variables:
Required Thickness:
Tr [in] =
Thickness Check
Maximum Pressure: 
Po [psi] =
Pressure Check


P = Design Pressure

L = inside spherical or crown radius

S = maximum allowable stress value (provided from ASME BPVC Tables HF-300.1 and HF-300.2

E = lowest efficiency of any joint in the head

tn = wall thickness before forming operations

t = wall thickness

tr = Required design thickness

Po = maximum operating pressure

References: ASME Boiler and Pressure Vessel Code