In summary, the relationship between applied torque $\mathrm{T}$ and shear stress $\mathrm{\tau }$ is given by the torsion formula:

${\mathbf{\tau }}_{\mathbf{max}}\mathbf{=}\frac{\mathbf{Tc}}{\mathbf{J}}$

and the angle of twist $\mathrm{\varphi }$ for a prismatic shaft with a circular cross section is found from the following equation:

$\mathbf{\varphi }\mathbf{=}\frac{\mathbf{TL}}{\mathbf{JG}}$