The perpendicular axis theorem, also called the plane figure theorem, is a result used to compute the moment of inertia of a flat, two dimensional object known as a planar lamina. It states that the moment of inertia of such an object about an axis perpendicular to its plane equals the sum of the moments of inertia about two axes that lie within the plane itself, are perpendicular to each other, and intersect at the point where the perpendicular axis passes through the object. The theorem applies only to objects that lie entirely within a single plane. It is often used together with the parallel axis theorem to calculate the polar moment of inertia for a variety of shapes, and when a planar object has enough rotational symmetry that its two in plane moments of inertia are equal, the theorem simplifies further into a particularly useful relationship between the perpendicular moment and either of the equal in plane moments.
Facts
StatementFor a planar lamina, the moment of inertia about an axis perpendicular to its plane equals the sum of the moments of inertia about two mutually perpendicular axes in the plane meeting at the point where the perpendicular axis passes through (Iz = Ix + Iy). 1 Classification
Statement Form Connections
Has Statement Form
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.
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. Perpendicular axis theorem (Wikipedia)
Main statementQuote, Main statement
for a planar lamina the moment of inertia about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia about two mutually perpendicular axes in the plane of the lamina, which intersect at the point where the perpendicular axis passes through.
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