Shaft Angle of Twist Calculator: worked example
This example is generated from PROFENG's own default input set and the implemented relationship. It is not copied from a cited publication.
Relationship
θ = TL/(JG)
This calculator determines angle of twist from torque, shaft length, solid shaft diameter, shear modulus. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
Inputs
- Torque (torque) = 1,000 N·m
- Shaft length (length) = 2 m
- Solid shaft diameter (diameter) = 50 mm
- Shear modulus (shearModulus) = 80 GPa
Working
(1000)*(2)/((Math.PI*Math.pow((50)/1000,4)/32)*((80)*1e9))*180/Math.PI = 2.334 deg
Angle of twist: 2.334 deg
Assumptions and limits
- Loads and geometry are represented by the idealized relationship shown.
- Material behavior is treated according to the simple formula, typically linear-elastic where relevant.
- Units and section properties are consistent with the displayed equation.
- Shaft is straight, circular and of uniform diameter over the modeled length.
- Material is linear elastic in shear and deformation is small.
- Torque is represented as constant over the modeled segment.
Formula source and acknowledgement
Richard G. Budynas, Keith J. Nisbett, Shigley's Mechanical Engineering Design in SI Units, 11th, 2020, McGraw Hill. Credit belongs to the cited author(s)/publisher; PROFENG presents its own implementation and does not imply endorsement.
Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek, Mechanics of Materials, 8th, 2020, McGraw Hill. Credit belongs to the cited author(s)/publisher; PROFENG presents its own implementation and does not imply endorsement.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks and an independent implementation where applicable.
This worked example is for engineering screening and education. Replace defaults with traceable project data and confirm the method, assumptions, standards and equipment information before design, procurement or operation.