How this calculator works
Choose the missing quantity in the small-deformation torsion law. J is the Saint-Venant torsion constant; for a circular section it equals the polar second moment. A non-circular section needs its torsion constant rather than its polar moment. The shaft is prismatic, linearly elastic and free to warp. Reverse calculations need a nonzero measured twist when it is a divisor.
Formula
phi = T L / (G J), with phi in radians and J in m4.
Worked example
A shaft with T = 100 N m, L = 2 m, G = 80 GPa and J = 0.000001 m4 twists 0.0025 rad, about 0.14324 degrees.
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Frequently asked questions
Which angle unit enters the formula?
The engine converts your angle to radians before calculation.
Can this model handle a stepped shaft?
Calculate each uniform segment separately and add signed twists, taking care with torque directions.
Does a larger diameter reduce twist?
Yes. For a solid round shaft J grows with the fourth power of diameter, so diameter strongly affects rigidity.