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`V = pi a b ((2 c)/3 - x + x^3/(3c^2))`
Enter a value for all fields
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)