Shaft Torsion Calculator

Inputs

Shaft type

Solid uses Di = 0. Hollow subtracts the entered bore from the polar moment.

Applied torque (T)

Torque carried by the shaft.

N·m

Shaft length (L)

Uniform shaft length over which the twist is calculated.

Outside diameter (Do)

Outside diameter of the circular shaft.

Shear modulus (G)

Steel is about 79 GPa; aluminium is about 26 GPa.

GPa

Allowable shear stress (tau_allow)

Static allowable shear stress used for torque capacity and safety factor.

MPa

Default result

Maximum shear stress(tau_max)

40.74MPa

Pass

Below the entered allowable shear stress.

Also computed

Angle of twist(theta)1.182°

Twist is below 2 deg/m; verify against your machine alignment limit.

Polar moment J(J)61.36cm⁴

Torque at allowable stress(T_allow)1,963N·m

Stress safety factor(N)1.96

Based on the entered static allowable shear stress.

Effective inside diameter(Di)0mm

Elastic torsional shear stress varies linearly with radius and reaches the reported maximum at the outside surface.

Method notes 3 notes

Circular-shaft elastic torsion: J = pi*(Do^4 - Di^4)/32, tau_max = T*(Do/2)/J, and theta = T*L/(G*J).
Stress is assumed to vary linearly from zero at the centerline to the maximum at the outside surface.
This does not model keyways, shoulders, splines, welds, stress concentrations, fatigue, residual stress, non-circular warping or bearing/support flexibility.