Area Moment of Inertia

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Calculate the second moment of area for structural cross-sections.

Section Dimensions

Section Shape

Base Width (b)

Height (h)

Results

Enter cross-section dimensions

About this calculator

Overview

The area moment of inertia, also known as the second moment of area, is a geometric property of a beam's cross-section which describes its resistance to bending and deflection. It is purely dependent on the shape and distribution of the area around an axis.

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Pro Tips

The height (h) is the most critical dimension for stiffness, as it is usually cubed in inertia formulas.
The result is calculated relative to the centroidal axis parallel to the base.
SI units are typically m⁴ or mm⁴; US units are usually in⁴.

Fun Facts

"I-beams are designed with most of their material in the top and bottom flanges because that material is furthest from the neutral axis, providing the highest possible inertia-to-weight ratio."
"If you double the height of a rectangular beam, it becomes 8 times stiffer, while doubling the width only makes it 2 times stiffer."
"The 'polar' second moment of area is used for calculating resistance to torsion (twisting)."