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
| Symbol | Meaning | Unit |
|---|---|---|
m | Torque | N·m |
d | Diameter | mm |
T | Shear stress | MPa |
W | Section modulus | mm³ |
A | Angle | mrad/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.