T = torque (N·mm)
Solid circular shaft torsion
Relates torque, selected allowable shear stress and diameter for a solid circular shaft under pure torsion.
FORMULA REFERENCE
T = πτd³ / 16
Relates torque, selected allowable shear stress and diameter for a solid circular shaft under pure torsion.
Variables and units
Keep each value in the units shown below before substituting it into the displayed relation. Convert first rather than mixing unit systems inside one calculation.
τ = selected allowable shear stress (N/mm²)
d = shaft diameter (mm)
WORKED EXAMPLE
Calculate the stated condition, then interpret its boundary.
Known values
- T = 98,793 N·mm
- τ = 37.5 N/mm²
Substitution: d = ∛(16 × 98,793 / (π × 37.5))
Calculated result: d = 23.7 mm
Engineering interpretation: Select an available size above 23.7 mm only after bending, fatigue, stiffness, keyway and manufacturing checks.
Conditions, limitations and review
- Solid circular shaft
- Pure torsion
- Selected allowable stress is source-controlled
Use this formula to understand or screen the stated engineering condition. A final design requires the governing standard, actual loads, material condition, manufacturing features and professional engineering judgement.
Source: J. E. Shigley et al., Mechanical Engineering Design, torsion of circular shafts.