Shaft Torsion Calculator

Estimate shear stress and angle of twist for a uniform solid circular shaft under a stated torque.

Model: uniform, solid circular shaft under one applied torque. Enter the actual shear modulus for the material and operating condition.

Maximum shear stress39.789 MPa5.771 ksi
Angle of twist1.443°0.02518 rad
Polar moment (J)251,327.412 mm⁴Solid circular section

Important: this is a linear-elastic, Saint-Venant torsion estimate. It does not check keyways, splines, hollow sections, stress concentration, fatigue, yield, critical speed, connections or combined loading.

Method

For a solid circular shaft, J = πd4/32, τmax = T(d/2)/J and θ = TL/(GJ).

Worked example

A 500 N·m torque applied to a 40 mm diameter, 1 m steel shaft with G = 79 GPa gives approximately 39.8 MPa shear stress and 1.44° of twist.

Important limits

This calculator applies to a uniform solid round shaft in linear elastic torsion only. It does not account for keyways, splines, hollows, combined bending, fatigue, dynamic effects or code-required margins.

References

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