Shaft Diameter Calculator
Sizing a Shaft From the Load It Has to Survive
A rotating shaft under torsion fails in shear along its cross-section, and the maximum shear stress it experiences depends entirely on its diameter — cubed. That steep relationship means small diameter changes have an outsized effect on strength, which is exactly why shaft sizing is worked backward from an allowable stress rather than guessed from experience alone.
The Formula
This is the solid-shaft torsion formula derived from maximum shear stress theory, where T is the applied torque and τallow is the material's allowable shear stress — typically a fraction of its yield strength after a safety factor is applied.
Worked Example
| Torque | Allowable Shear Stress | Minimum Diameter |
|---|---|---|
| 500 | 50 MPa | 37.07 mm |
| 150 | 60 MPa | 23.35 mm |
| 80 | 40 MPa | 21.68 mm |
Because diameter scales with the cube root of torque, doubling the torque only increases the required diameter by a factor of roughly 1.26, not 2 — but it increases the shaft's cross-sectional material and weight far more than that.
Where This Calculation Matters
- Drivetrain design — sizing shafts to safely carry the torque produced by a motor, engine, or gear reduction stage.
- Failure investigation — checking whether an existing shaft diameter provides adequate margin against a known operating torque.
- Material substitution — recalculating the required diameter when switching to a material with a different allowable shear stress.
How to Use This Calculator
- Enter Torque (N.mm) — the torque the shaft must transmit.
- Enter Allowable Shear Stress (MPa) — the material's safe working shear stress.
- Select Calculate to get the minimum required shaft diameter.
Related Calculations
Once torque is known from a gear or pulley stage, bring it here directly from the Gear Design Calculator or the Power Transmission Calculator.