# Ellipsoid - Volume

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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:

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⋅a3  where a is the radius (r) of the sphere.