🌀 Mass Moment of Inertia Calculator
Calculate the mass moment of inertia for common rigid body shapes rotating about their central axis.
What mass moment of inertia is
The mass moment of inertia describes how resistant an object is to changes in its rotational motion, similar to how mass resists changes in linear motion. It depends on both the mass and how that mass is distributed relative to the axis of rotation.
The formulas used
This calculator uses standard textbook formulas for common shapes rotating about their central axis: solid cylinder/disk I = ½mr², solid sphere I = (2/5)mr², hollow spherical shell I = (2/3)mr², thin rod about its center I = (1/12)mL² (using twice the entered radius as length), and thin ring/hoop I = mr².
These are idealized formulas assuming uniform density and a rigid body; real objects with non-uniform mass distribution will differ.