Perpendicular : Moment of Inertia (Parallel Axis Theorem) Calculator

Calculate perpendicular moment of inertia by using simple parallel axis theorem / formula calculator online.

In physics, the parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, after Christiaan Huygens and Jakob Steiner, can be used to determine the mass moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between the axes.

Suppose a body of mass m is made to rotate about an axis z passing through the body's centre of gravity. The body has a moment of inertia I_cm with respect to this axis. The parallel axis theorem states that if the body is made to rotate instead about a new axis z′ which is parallel to the first axis and displaced from it by a distance d, then the moment of inertia I with respect to the new axis is related to _cm by I = Icm + md²

The parallel axis theorem can be applied with the stretch rule and perpendicular axis theorem to find moments of inertia for a variety of shapes.