Area moment of inertia

Engineering Fundamentals


The area moment of inertia (also referred to as second moment of area) is a geometrical property of a shape describing the distribution of points around an axis. In classical mechanics it is used as a measure of a body’s resistance against bending.

Note that next to the area moment of inertia, the polar moment of inertia is used as a measure of a body’s resistance to torsion (see Beam theory: Torsion sheet). Also, the area moment of inertia should not be confused with the mass moment of inertia, which is used as a measure of how an object resists rotational acceleration about a particular axis (see Mass moment of inertia sheet). The area moment of inertia is typically denoted with an I and has an axis that lies in the plane, the polar second moment of inertia is typically denoted with a J and has an axis perpendicular to the plane.

Cross-sectionArea moment of inertia
Area moment of inertia shape$$I_x=I_y=\frac{\pi}{4}r^4$$
Area moment of inertia shape$$I_x=I_y=\frac{\pi}{4}\left(r_o^4-r_i^4\right)$$
Area moment of inertia shape$$I_x=\frac{{wh}^3}{12}$$
Precision Point - Beam Theory Torsion$$I_x=\frac{w_oh_o^3-w_ih_i^3}{12}$$
Area moment of inertia shape$$I_x=\frac{wh^3}{12}-\frac{\left(w-t_2\right)\left(h-2t_1\right)^3}{12}$$
Area moment of inertia shape$$I_x=\ \frac{wh^3}{36}$$
Area moment of inertia shape$$I_x=\frac{\pi}{4}{r_1r}_2^3$$

Tech Support

Please submit a message and we will come back to you on short notice.

Precision Point sheet download

Please fill in your details to receive the requested Precision Point sheet.

We use cookies to ensure to give you the best experience on our website. If you continue to use this site we will assume that you are okay with it.