Suppose that normal and shear stresses are known with respect to two orthogonal coordinate axes x and y. Stresses with respect to orthogonal axes n and t oriented at an angle relative to the x axis may be determined from the equations:

${\sigma }_n=\frac{{\sigma }_x+{\sigma }_y }{2}+\frac{{\sigma }_x-{\sigma }_y }{2}\cos 2\theta + {\tau }_{xy}\sin 2\theta$

${\sigma }_t=\frac{{\sigma }_x+{\sigma }_y }{2}-\frac{{\sigma }_x-{\sigma }_y }{2}\cos 2\theta - {\tau }_{xy}\sin 2\theta$

${\tau }_{nt}=-\frac{{\sigma }_x-{\sigma }_y }{2}\sin 2\theta + {\tau }_{xy}\cos 2\theta$