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`V = pi/3 [2hR^2 - (2a^2+c^2+2aR)(R-h)+3a^2csin^(-1)((R-h)/(R-a))]`

Enter a value for all fields

The **Torispherical Head Volume and Height** calculator computes the volume of an torispherical head based on the crown radius (R), knuckle radius (a) and the Diameter (D). It also computes the head height (h).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**R**) Crown Radius - (
**a**) Knuckle Radius - (
**D**) Diameter of the head

**Torispherical Head Volume (V) and Height (h):** The volume is returned in cubic meters and the height is returned in meters. However, these can be automatically converted to compatible units via the pull-down menu. *Cylindrical Tank with Torispherical Heads*

- Capacity of a Dished End Tank
- Volume and Diameter of a Torispherical Head
- Volume and Head Height of a Torispherical Head
- Volume of a Torispherical Head Cylindrical Tank
- Mass of the Contents of Torispherical Head Tank
- Storage Capacity of a Rectangular Tank
- Above Ground Storage Tank Capacity
- Storage Capacity of a Cylindrical Tank

The formula for the volume of an Torispherical Head is as follows:

`V = π/3[2⋅h⋅R²-(2a² + c² + 2aR)(R-h)+3a²c sin‾¹( (R-h)/(R-a))]`

where:

- V is the volume of the Torispherical Head
- R is the crown radius
- h is the head height.
- a is the knuckle radius

The value of c is computed from R, h and a as follows:

`c = sqrt( (R-a)² - (R-h)² )`

solving for h:

`h = R - sqrt((R-a)^2 - c^2)`

We also know that:

D = 2(c+a)

which means that:

c = D/2 - a