Rectangle Moment of Inertia Calculator

About this calculator

The second moment of area (commonly called the moment of inertia of a cross-section, though distinct from mass moment of inertia) measures how a shape's material is distributed relative to a bending axis, and it directly governs a beam's resistance to bending deflection. For a rectangular section of width b and height h about its centroidal axis, the formula is I = bh³/12 — the cube on the height reflects why standing a beam on edge (tall and narrow) resists bending far more than laying it flat, even with identical cross-sectional area.

This calculator takes a rectangle's width and height and returns its moment of inertia along with the section modulus (S = I/c, where c is the distance to the extreme fiber), which converts directly into bending stress via the flexure formula. Structural and mechanical engineers, and students working through statics or mechanics of materials coursework use these values to size beams and joists, verify that a section can carry a design load, and compare stiffness between different rectangular profiles.