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.
Facts
StatementThe moment of inertia or second moment of area of a rigid body about any axis can be found from its moment of inertia about a parallel axis through the center of gravity and the perpendicular distance between the axes. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Parallel axis theorem (Wikipedia)
Lead sentenceQuote, Lead sentence
can be used to determine the 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.
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