Moment of Inertia of Particles Calculator

About this calculator

The moment of inertia of particles calculator computes the rotational inertia of a system of discrete point masses about a chosen axis using I = Σ mᵢrᵢ², summing each particle's mass mᵢ multiplied by the square of its perpendicular distance rᵢ from the axis of rotation. Unlike a continuous rigid body, where you'd need to integrate a density function over the shape, a set of point particles reduces the problem to simple addition.

Moment of inertia is the rotational analog of mass in Newton's second law — it determines how much torque is needed to achieve a given angular acceleration (τ = Iα) — and the particle-sum form is the building block used to derive the standard formulas for rods, disks, and spheres by treating the object as infinitely many point masses. Mechanical and aerospace engineering students, and engineers modeling multi-body systems like flywheels, satellites, or linkages use this calculator to get I directly from a list of masses and distances instead of deriving it from scratch.