Parallel Axis Theorem

The parallel axis theorem, also called the Huygens-Steiner theorem after Christiaan Huygens and Jakob Steiner, is a result used to find the moment of inertia of a rigid body about any axis. It states that the moment of inertia about an axis parallel to one running through the body center of gravity equals the moment of inertia about that central axis, plus the total mass of the body multiplied by the square of the distance between the two axes. The theorem also applies in the same form to the second moment of area, a related quantity used in engineering. It provides a way to compute the moment of inertia about an off center axis directly from the already known moment of inertia about the center of gravity, without repeating the full calculation.