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# Ellipsoid - Volume

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Equation / Last modified by KurtHeckman on 2019/04/14 01:31
`V = `

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vCalc.Ellipsoid - Volume

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The **Volume of an Ellipsoid** formula, V = ^{4}/_{3}⋅π⋅a⋅b⋅c, computes the volume of an ellipsoid with semi-axes of lengths a, b, and c.

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

- (
**a**) semi-axis a. - (
**b**) semi-axis b. - (
**c**) semi-axis c.

**Volume of an Ellipsoid (V):** The volume of the ellipsoid (**v**) 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

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

V = ^{4}/_{3}⋅π⋅a⋅b⋅c

where:

- V is the volume of the ellipsoid
- a, b and c are the lengths of the semi-axes

An ellipsoid is the most general shape in the class that includes:

- ellipsoid
- oblate spheroid
- sphere

Note that in each progressing case the number of axes with different lengths reduces from 3 in an ellipsoid, to 2 in an oblate spheroid, to one uniform radius in a sphere. Note that this formula is the equivalent to the volume of a sphere:

V =^{4}/_{3}⋅π⋅a⋅b⋅c

V =^{4}/_{3}⋅π⋅a⋅a⋅a

V =^{4}/_{3}⋅π⋅a^{3}where a is the radius (r) of the sphere.

#### 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.**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.

#### Volume Calculators

- Volume of a Cube
- Volume of a Box
- Volume of a Cone
- Volume of a Cone Frustum
- Volume of a Cylinder
- Volume of a Slanted Cylinder
- Volume of a Triangular - 3 sided column
- Volume of a Quadrilateral - 4 sided column
- Volume of a Pentagon - 5 sided regular column
- Volume of a Hexagon - 6 sided regular column
- Volume of a Heptagon - 7 sided regular column
- Volume of a Octagon - 8 sided regular column
- Volume of a Nonagon - 9 sided regular column
- Volume of a Decagon - 10 sided regular column
- Volume of a Hendecagon - 11 sided regular column
- Volume of a Dodecagon - 12 sided regular column
- Volume of a Paraboloid
- Volume of a Polygon based Pyramid
- Volume of a Pyramid Frustum
- Volume of a Sphere
- Volume of a Oblate Spheroid
- Volume of a Ellipsoid

This equation,

**Ellipsoid - Volume**, is used in 5 calculators.