Calculate the rotational (torsional) stiffness of a component based on applied torque and resulting angular deflection.
Last updated: March 2026 | By ForgeCalc Engineering
Rotational stiffness (or torsional stiffness) is a measure of the resistance of an object to angular deformation. It is defined as the ratio of applied torque to the resulting angle of rotation.
In mechanical engineering, high rotational stiffness is often desirable for precision components like shafts, couplings, and chassis to ensure accurate motion transfer and minimize unwanted vibrations or "slop" in a system.
Where:
• k_θ is the rotational stiffness (N·m/rad)
• T is the applied torque (N·m)
• θ (theta) is the angular deflection in radians
In physics and engineering formulas, radians are the standard unit for angle because they are based on the geometry of a circle (arc length / radius), which simplifies many mathematical relationships.
Stiffness depends on both the geometry of the part and the material's Shear Modulus (G). For a solid shaft, k_θ = (G × J) / L, where J is the polar moment of inertia and L is the length.
Stiffness is about how much an object deforms under load (elasticity), while strength is about how much load it can take before failing or permanently deforming (plasticity).
Backlash is the clearance or 'lost motion' in a mechanical system (like gears) when the direction of motion is reversed. It is different from rotational stiffness, which is the elastic deformation under load.
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