Second Moment of Area (Rect.)

The second moment of area measures how the shape of a cross-section is distributed about a bending axis, and for a rectangle it increases very strongly with height because the outer fibers carry most of the bending effect. The factor h^3 appears because material farther from the neutral axis contributes disproportionately to resisting bending, while the width b contributes linearly since widening the section adds material evenly across the span. This result comes from integrating y^2 across the rectangular area about its centroidal axis, which is why the units are length to the fourth power.

Use this formula when you need the bending stiffness of a rectangular cross-section in beam design, stress analysis, or deflection calculations. It is also useful for comparing design changes, such as whether increasing depth or width gives a bigger gain in stiffness.

• Using the wrong dimension for h: the height is the dimension perpendicular to the bending axis, and it is the one that gets cubed
• Forgetting that the formula gives the centroidal second moment of area, not the polar moment of area
• Mixing units, such as entering dimensions in mm but expecting the answer in m^4 without converting