Assuming that the moments and product of inertia of an area are known about orthogonal coordinate axes $\mathrm{x}$ and $\mathrm{y}$, the moments and product of inertia about new axes $\mathrm{x}\text{'}$ and $\mathrm{y}\text{'}$ may be determined from the equations:

${\mathrm{I}}_{\mathrm{x}\text{'}}=\frac{{\mathrm{I}}_{\mathrm{x}}+{\mathrm{I}}_{\mathrm{y}} }{2}+\frac{{\mathrm{I}}_{\mathrm{x}}-{\mathrm{I}}_{\mathrm{y}} }{2}\cos 2\mathrm{\theta } - {\mathrm{I}}_{\mathrm{xy}}\sin 2\mathrm{\theta }$

${\mathrm{I}}_{\mathrm{y}\text{'}}=\frac{{\mathrm{I}}_{\mathrm{x}}+{\mathrm{I}}_{\mathrm{y}} }{2}-\frac{{\mathrm{I}}_{\mathrm{x}}-{\mathrm{I}}_{\mathrm{y}} }{2}\cos 2\mathrm{\theta } + {\mathrm{I}}_{\mathrm{xy}}\sin 2\mathrm{\theta }$

${\mathrm{I}}_{\mathrm{x}\text{'}\mathrm{y}\text{'}}=\frac{{\mathrm{I}}_{\mathrm{x}}-{\mathrm{I}}_{\mathrm{y}} }{2}\sin 2\mathrm{\theta } + {\mathrm{I}}_{\mathrm{xy}}\cos 2\mathrm{\theta }$