Torsion in Shaft Calculator
When a shaft is twisted by an applied torque, it develops shear stress that varies from zero at the centre (the neutral axis) to a maximum at the outer surface, along with an angular twist along its length. This calculator works out both the shear stress and the angle of twist from the applied torque, shaft length, diameter, and material properties — useful for checking that a shaft is adequately sized before it yields or twists more than the design allows.
For related shaft calculations, see our Power, Torque and Speed Calculator and Young's Modulus Calculator.
When a shaft is subjected to a torque or twisting, a shearing stress is produced in the shaft.
The shear stress varies from zero in the axis to a maximum at the outside surface of the shaft.
SOLID SHAFT SHEAR STRESS AND ANGULAR DEFLECTION CALCULATOR
Enter moment, diameter and length values, select your material and units as required. Your result will display.
HOLLOW SHAFT SHEAR STRESS AND ANGULAR DEFLECTION CALCULATOR
Enter moment, diameter and length values, select your material and units as required. Your result will display.
RELATED PAGES
FREQUENTLY ASKED QUESTIONS
Why is shear stress zero at the centre of the shaft?
Torsional shear stress is proportional to the radial distance from the shaft's axis, so it's zero exactly at the centre and increases linearly out to a maximum at the outer surface — this is why hollow shafts can be an efficient way to save weight, since the lightly stressed material near the centre contributes little to torsional strength anyway.
What's the difference between shear stress and angle of twist?
Shear stress tells you whether the shaft will yield or fail under the applied torque; angle of twist tells you how much the shaft rotates elastically along its length under that same torque, which matters for applications where precise angular positioning or stiffness is important, even if the stress itself is well within safe limits.
Does shaft diameter or length have a bigger effect on twist?
Diameter, by far — angle of twist is inversely proportional to the fourth power of diameter but only directly proportional to length, so a relatively small increase in diameter reduces twist much more effectively than shortening the shaft.
Affiliate Partners
Help support us by using our affiliate links below.
Link To Amazon.com
Link To Amazon.co.uk