Rotational Stiffness Calculator

What Is Rotational Stiffness?

Rotational stiffness (torsional stiffness) measures how much torque is required to produce a unit angular displacement. It is the rotational analogue of linear spring stiffness and is essential for shafts, springs, and structural joints in torsion.

Rotational Stiffness Formula

\(T\) is torque in newton-meters (N·m) and \(\theta\) is angular displacement in radians. If displacement is given in degrees, convert with \(\theta_{\text{rad}} = \theta_{\text{deg}} \times \pi/180\) before dividing.

Example: 50 N·m applied over 0.05 rad gives \(k = 50 / 0.05 = 1000\) N·m/rad.

Applications

Engineers use rotational stiffness to size torsion bars, coupling elements, and machine tool spindles. Higher stiffness means less angular deflection for a given torque, which improves precision and reduces vibration.