How this calculator works
Rotational stiffness is the slope of torque against angular deflection for a linear elastic torsional element. Applied holding torque and deflection use the same sign here; the internal restoring torque has the opposite sign. Stored energy is the area under the linear torque-deflection curve. Use a tangent stiffness for a nonlinear spring only over the range where that approximation is valid.
Formula
tau_applied = k_theta theta; k_theta = tau/theta; U = k_theta theta²/2. Deflection is converted to radians.
Worked example
A 12 N m holding torque causing 0.5 rad deflection gives stiffness 24 N m/rad and stored energy 3 J. A 100 N m/rad spring twisted 0.2 rad needs 20 N m.
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Frequently asked questions
Is rotational stiffness a torque?
No. It is torque per angle, typically N m/rad.
Can I enter degrees?
Yes. The angle input converts degrees to radians before applying the stiffness relationship.
Does this calculate shaft stiffness from geometry?
No. Enter measured torque and deflection or a known stiffness. Shaft shear modulus and polar area moment need a separate model.