Shaft Torsion Calculator
Enter torque T, length L, shear modulus G, outer diameter dₒ, and inner diameter dᵢ; use dᵢ=0 for a solid shaft.
A QUICK WALKTHROUGH
How to use this tool
- Use m for lengths, N·m for torque, and Pa for modulus.
- Review polar moment, shear stress, signed twist, and torsional stiffness.
Formula and source
J = π(dₒ⁴ − dᵢ⁴)/32; τmax = |T|(dₒ/2)/J; θ = TL/(GJ); kθ = GJ/L. Source: NASA-hosted Mechanical Design Reliability Handbook, torsion relationship: https://extapps.ksc.nasa.gov/Reliability/Documents/Mechanical-Design-Reliability-Monograph.pdf
Input limits and scope
Finite T; L>0, G>0, dₒ>0, and 0≤dᵢ<dₒ. Outputs: J (m⁴), maximum shear stress (Pa), signed angle (rad and degrees), and torsional stiffness (N·m/rad). Assumes a straight, prismatic circular shaft, uniform torque, and linear-elastic Saint-Venant torsion; excludes noncircular warping, stress concentrations, plasticity, fatigue, buckling, and code factors.
GOOD TO KNOW
Common questions
Does this cover noncircular sections or stress concentrations?
No. Warping, stress concentrations, plasticity, fatigue, buckling, and code factors are outside its scope.
Is a shear-modulus default supplied?
No. Enter the project-specific material property.