How this calculator works
Torsional stiffness is torque divided by angular displacement in radians. For a uniform elastic shaft it equals shear modulus times the Saint-Venant torsion constant divided by length. For non-circular shafts, use the torsion constant and account separately for restrained warping. Stiffness is reported explicitly in N m/rad; torque-angle unit choices are converted before division.
Formula
k = T/phi = GJ/L; T = k phi.
Worked example
A torque of 100 N m causing 0.02 rad twist gives k = 5000 N m/rad. G = 80 GPa, J = 0.000001 m4 and L = 2 m give k = 40000 N m/rad.
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Frequently asked questions
How does stiffness differ from rigidity?
Torsional rigidity is GJ. Stiffness GJ/L includes the member length.
Can I enter degrees for twist?
Yes. The angle input converts degrees to radians, and the reported stiffness stays per radian.
How do shafts in series combine?
For the same transmitted torque, their twists add, so reciprocal stiffnesses add.