Paritian

Mechanics

Shaft Torsion Stress Calculator

Shear stress and section modulus of a solid round shaft under torque.

Results

Shear stress 47.157 MPa
Section modulus 5301.4 mm³
Angle 0.5895 mrad/m

What this tool does

Torsional stress falls with the cube of the diameter, so a shaft only 25 % thicker carries roughly twice the torque at the same stress. The twist figure assumes steel with a shear modulus of 80 GPa and no stress concentrations from keyways or steps.

Formula

τ = 16 × M ÷ (π × d³)

Variables

SymbolMeaningUnit
mTorqueN·m
dDiametermm
TShear stressMPa
WSection modulusmm³
AAnglemrad/m

Worked example

  • Torque250 N·m
  • Diameter30 mm
  • Shear stress47.157 MPa
  • Section modulus5301.4 mm³
  • Angle0.5895 mrad/m

Limitations

  • For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
  • The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.