MoI - torus around axis in the plane

The Moment of Inertia of a Torus calculator computes the moment of inertia of a torus of uniform density with outer radius a and inner radius b about a line through the center of mass lying in the plane of the torus.

INSTRUCTIONS: Choose units and enter the following:

• (M) Mass of the torus
• (a) Inner Radius
• (b) Outer Radius

Torus Moment of Inertia (MoI): The calculator returns the moment of inertia.

The Math / Science

The formula for the moment of inertia of a torus about a line through the center of the ring and center of mass is:

      MoI = (M(9•a²-10•a•b+5•b²))/4

where:

• M = Mass of torus
• a = inner radius of torus
• b = outer radius of torus