Shaft torsional stress and twist calculator
Helps check whether a shaft diameter is enough to carry a torque. Enter the torque, diameter, length and shear modulus.
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How to use it
- Enter torque, shaft diameter, shaft length and shear modulus.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
τ = 16 T ÷ (π d³). J = π d⁴ ÷ 32. Angle of twist θ = T L ÷ (G J) in radians.
Example
Inputs: Torque = 100 N·m, Shaft diameter = 20 mm, Shaft length = 1,000 mm, Shear modulus = 80 GPa. Result: Maximum shear stress: 63.662 MPa; Angle of twist: 4.5595 °; Polar moment of inertia: 15,707.96 mm⁴.
Limits and caveats
- For a solid round shaft only; ignores stress concentration at keyways and shoulders.
- Does not include combined bending with torsion.
Questions about this tool
What is the shear modulus of steel?
About 79 to 80 GPa for most steels.
Where is the stress highest?
At the outer surface of the shaft; it is zero at the centre.
How do I choose a diameter?
Keep the calculated stress below the allowable shear stress of the material divided by a safety factor suited to your use.