Ellipsoid Cap - Volume

The Volume of an Ellipsoid Cap calculator computes the volume of an ellipsoid cap where the semi-axes of the ellipsoid are a, b, and c, and the height of the cap is h.

INSTRUCTIONS:  Choose units and enter the following:

• (a)  semi-axis a.
• (b)  semi-axis b.
• (c)  semi-axis c.
• (h) height of the cap

Volume of an Ellipsoid Cap (V): The volume is returned in cubic meters. However, the volume can be automatically converted to other volume units (e.g. cubic feet, gallons, barrels) via the pull-down menu. 

The Math / Science

An ellipsoid is defined by three semi-axes.  In the diagram they are labeled a, b and c.

The formula for the volume of an ellipsoid cap  is as follows:

           `V = π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))`

where:

• V is the volume of the ellipsoid cap
• a, b and c are the lengths of the semi-axes
• x = c - h and h is the height of the ellipsoid cap

Ellipsoid Calculator

• Ellipsoid - Volume computes the volume of an ellipsoid based on the length of the three semi-axes (a, b, c)
• Ellipsoid - Surface Area computes the surface area of an ellipsoid based on the length of the three semi-axes (a, b, c)
• Ellipsoid - Mass or Weight computes the mass or weight of an ellipsoid based on the length of the three semi-axes (a, b, c) and the mean density.
• Ellipsoid Cap - Volume computes the volume of a section of an ellipsoid.
• Oblate Spheroid - Volume computes the volume of an Oblate Spheroid based on the length of the two semi-axes (b, c)
• Oblate Spheroid- Surface Area computes the surface area of an Oblate Spheroid based on the length of the two semi-axes (b, c)
• Oblate Spheroid- Mass or Weight computes the mass or weight of an Oblate Spheroid based on the length of the two semi-axes (b, c) and the mean density.
• Sphere - Volume computes the volume of a sphere based on the length of the radius (a)
• Sphere  - Surface Area computes the surface area of a sphere based on the length of the radius (a)
• Sphere  - Mass or Weight computes the mass or weight of a sphere based on the length of the radius (a) and the mean density.
• Circular - Volume: Computes the volume of a column with a circular top and bottom and vertical sides.
• Circular - Mass: Computes the mass/weight of circular volume based on its dimensions and mean density.
• Elliptical Volume: Computes the volume of a column with an elliptical top and bottom and vertical sides. 
• Elliptical - Mass: Computes the mass/weight of an elliptical volume based on its dimensions and mean density.
• Ellipse Vertical Chord from Edge (VE): Computes the length of the vertical chord of an ellipse based on distance from the edge.
• Ellipse Vertical Chord from Center (VC): Computes the length of the vertical chord of an ellipse based on distance from the center.
• Ellipse Horizontal Chord from Edge (HE): Computes the length of the horizontal chord of an ellipse based on distance from the edge.
• Ellipse Horizontal Chord from Center (HC): Computes the length of the vertical chord of an ellipse based on distance from the center.
• Common Mean Density: Provides a lookup function to find the mean density of hundreds of materials (woods, metals, liquids, chemicals, food items, soils, and more)