Moment of Inertia Calculator

Moment of inertia (I) is the rotational equivalent of mass. It measures an object's resistance to angular acceleration. It depends on both mass and how that mass is distributed relative to the axis of rotation: I = Σm_i·r_i². Units are kg·m².

The parallel axis theorem states I = I_cm + md², where I_cm is the moment of inertia about the center of mass, m is the total mass, and d is the distance between the two parallel axes. It lets you find I about any axis parallel to a known one.

The radius of gyration k = √(I/m) is the distance from the rotation axis at which all the mass could be concentrated to give the same moment of inertia. It simplifies comparing rotational properties of different shapes.