The Shaft Diameter Calculator gives a preliminary solid-shaft diameter from transmitted torque, allowable shear stress and a chosen factor of safety. It is intended as a first sizing step, not a final shaft design.
Shaft diameter formula
For a solid circular shaft in pure torsion, the maximum shear stress relationship is:
d = [16TN/(πτ)]1/3
where T is torque in N·mm, τ is allowable shear stress in MPa (N/mm²), and N is the factor of safety applied to the selected allowable stress. The calculator converts torque entered in N·m to N·mm automatically.
How to use the calculator
- Enter transmitted torque in N·m.
- Enter the allowable shear stress in MPa.
- Enter the factor of safety.
- Calculate the preliminary shaft diameter.
Worked example
Suppose a shaft transmits 100 N·m, the selected allowable shear stress is 40 MPa, and the factor of safety is 2. The design torque is 200,000 N·mm. Substitution gives a preliminary diameter of about 29.4 mm. In production, this would normally be rounded to a practical standard diameter and then checked against the actual service loads.
What this calculation does not check
A torque-only calculation can be unsafe if it is treated as the final design. Real shafts may carry bending from gears, pulleys or couplings; fluctuating loads can create fatigue; keyways and shoulders introduce stress concentrations; and excessive torsional or bending deflection can affect alignment. Check combined bending and torsion, fatigue, critical speed where relevant, bearing fits, keyways, shoulders and manufacturability before releasing the design.
Common shaft-design mistakes
- Using motor torque without considering the transmission ratio.
- Ignoring shock or service loading.
- Choosing a diameter only from yield strength and ignoring fatigue.
- Forgetting the diameter reduction caused by keyways or other features.
- Checking stress but not shaft deflection or bearing alignment.
Related mechanical design guides
Shaft design for torsion and bending · Worked shaft diameter calculation · Bearing selection · Gear-train design
Important engineering note
This calculator is a preliminary sizing aid. Final dimensions should be verified against the applicable design code, material properties, loading spectrum, fatigue requirements, manufacturing process and company engineering standards.