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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 **Volume of an Torispherical Head** calculator computes the volume of an torispherical head (dish-head) based on the crown radius (R), knuckle radius (a) and the height (h).

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

- (
**R**) Crown Radius - (
**a**) Knuckle Radius - (
**h**) Height of the Head

**Volume of an Torispherical Head (V):** The volume is returned in cubic meters and the diameter is also returned in meters. However, these can be automatically converted to compatible units via the pull-down menu. The **diameter of the head** is also returned. The head height, knuckle radius and diameter are related. *Cylindrical Tank with Torispherical Heads* If you prefer to use the diameter and knuckle radius as inputs instead of head height, use the Volume and Head Height of a Torispherical Head calculator.

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
- c is a computed length (see below)

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

`c = sqrt( (R-a)² - (R-h)² )`

The Diameter (D) is simply:

D = 2(c+a)

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