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

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

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

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