Rotational Stiffness Calculator
Calculate rotational stiffness from applied torque and angular displacement in radians or degrees. Get instant k values free in your browser, no signup needed.
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
$$k = \frac{T}{\theta}$$\(T\) 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.
Frequently Asked Questions
What units does rotational stiffness use?
The SI unit is N·m/rad (newton-meters per radian). Some references use N·m/deg, but radians are standard in mechanics formulas.
How is rotational stiffness different from linear stiffness?
Linear stiffness relates force to linear displacement (N/m). Rotational stiffness relates torque to angular displacement (N·m/rad). Both describe resistance to deformation.
Can stiffness change with angle?
This calculator assumes small-angle linear behavior where \(k = T/\theta\) is constant. Large deformations or nonlinear materials need a tangent stiffness at each angle.
What if angular displacement is zero?
Division by zero is undefined. In practice, measure torque and displacement over a small but nonzero angle range.
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