Ellipsoid - Volume

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Equation / Last modified by KurtHeckman on 2019/04/14 01:31
vCalc.Ellipsoid - Volume

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.Ellipsoid.png

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.  Ellipsoid_OblateSpheroid_Sphere.png 

The Math / Science

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

           V = 4/3⋅π⋅a⋅b⋅c


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.

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