`I_3 = (2* "m" * "b" ^2) / 5`

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The Moment of Inertia of an Ellipsoid rotating about the Axis₃ calculator computes moment of inertia for axis₃, the  (the long axis, a, in the picture) based on the mass an the length of axis b.

INSTRUCTIONS: Choose units and enter the following:

• (m) This is the mass of the ellipsoid
• (b) This is the length of axis 1.

Moment of Inertia (I₃): The calculator returns the moment of inertia in kilograms per square meters. 

Ellipsoid Calculators

• Compute the Moment of Inertia of an Ellipsoid (Axis 3)
• Compute the Moment of Inertia of an Ellipsoid (Axis 1 or 2)
• Compute the Mass of an Ellipsoid
• Compute the Volume of an Ellipsoid
• Compute the Surface Area of an Ellipsoid

The Math / Science

The ellipsoid is defined by the lengths of its three Cartesian axes, where as described in the diagram, `b = c` and `a` lies along the `"axis"_3`.  The Moments of Inertia define the spin of an ellipsoid and have a real world example in the motion of a football. ¹  The formula for the moment of inertia of an ellipsoid around axis 3 is:

`I_3 = 2/5•m•b^2`

where:

• I₃ is the moment of inertia of an ellipsoid around axis 3
• m is the mass of the ellipsoid
• b is the length of the axis.

1. ^ On the Flight of the American Football