What is angle of twist?
When a circular shaft is loaded with torque, it twists along its length. The angle of twist tells engineers how much rotational deflection to expect, which matters for shaft stiffness, alignment, and fatigue design.
The formula
For a solid circular shaft, the angle of twist is θ = (T × L) ÷ (J × G), where T is torque, L is shaft length, G is the material’s shear modulus, and J is the polar moment of inertia, J = πd4 ÷ 32 for a solid round shaft of diameter d.
This formula assumes the shaft stays within its elastic limit and has a uniform circular cross-section along its length. Hollow shafts, stepped shafts, or non-circular sections need a modified J value. This calculator is for general engineering reference and educational purposes.
Last reviewed August 2026