Calculate angle of twist, torsional stiffness, and shear stress of a uniform solid or hollow circular shaft.
Set the inputs and run the calculation.
Evaluate torsional stiffness and shear stress of a uniform solid or hollow shaft.
Torque, shaft length, outside and optional inside diameter and shear modulus define behavior.
Length acts directly on twist, while diameter acts through polar moment J to the fourth power. A hollow section saves mass but loses stiffness if the wall becomes too thin.
Saint-Venant: φ = T·L/(G·J), with polar second moment J. Shear stress rises with radius and is maximum at the outside.
Doubling length doubles twist; increasing outside diameter strongly increases stiffness.
Sources and limits: Linear elasticity for circular sections; notches, keyways and plastic torsion are excluded.
Evaluate torsional stiffness and shear stress of a uniform solid or hollow shaft.
Mechanical calculators translate geometry and load into a response such as torque, stress, deflection, spring force or bearing life. The position of the load relative to the effective axis is often decisive.
Saint-Venant: φ = T·L/(G·J), with polar second moment J. Shear stress rises with radius and is maximum at the outside.
Torque, shaft length, outside and optional inside diameter and shear modulus define behavior. Length acts directly on twist, while diameter acts through polar moment J to the fourth power. A hollow section saves mass but loses stiffness if the wall becomes too thin.
Enter torque, shaft length, outside diameter (and inside diameter for a hollow shaft) and the material's shear modulus. The calculator returns twist angle and maximum shear stress at the outer surface.
Doubling length doubles twist; increasing outside diameter strongly increases stiffness.
Length acts directly on twist, while diameter acts through polar moment J to the fourth power. A hollow section saves mass but loses stiffness if the wall becomes too thin. The result shows the idealized component response for the selected load case. A small change in diameter, height, length or load can have a large effect because of power laws.
Torque in N·m, length and diameter in millimetres, shear modulus in MPa, twist angle in degrees.
Estimating torsional stiffness for control or accuracy requirements, or comparing solid and hollow shafts of the same outside diameter for weight and stiffness.
Linear elasticity for circular sections; notches, keyways and plastic torsion are excluded.
Common mistake: Don't forget shear stress is maximum at the outer radius and zero at the shaft axis – a hollow shaft therefore uses material more efficiently than a solid shaft of the same outside diameter. This model assumes a uniform, notch-free shaft; shoulders and keyways must be assessed separately.
Polar second moment of area is barely affected by material near the axis, since it contributes little to torsional stiffness there; material at the outer radius contributes strongly instead.
Twist angle is proportional to length – a shaft twice as long under otherwise identical conditions twists twice as far.
No, the keyway weakens the section and creates a notch-stress concentration that this pure circular-section torsion model does not capture.
The calculator uses Saint-Venant torsion of a circular shaft and supports stiffness assessment after preliminary shaft sizing.
Notches, keyways, shoulders, non-circular sections, restrained warping, plasticity, and fatigue are outside scope.