Shaft diameter under torsion
Minimum shaft diameter from torque and allowable shear stress; optionally check a chosen diameter.
Calculator
Shaft diameter under torsion
Minimum shaft Ø that keeps τ = 16T/(πd³) at or below an allowable shear stress.
Torque and material
Result
- Minimum solid diameter d_min
- 18.53 mm
Check a chosen diameter (optional)
Advanced: hollow circular shaft check
Check a chosen section using the same torque and allowable stress. Does not size a minimum hollow diameter. τ = 16T·Dₒ/[π(Dₒ⁴−Dᵢ⁴)] with T in N·mm. Elastic pure torsion of a uniform concentric circular section only; no local buckling, fatigue, stress concentrations or combined loading.
Wiley / Philpot — J = π(Dₒ⁴−Dᵢ⁴)/32 · Formula checked: 2026-10-08
No hollow-shaft result: enter valid diameters, torque and allowable stress. Extreme values may prevent reliable numerical results.
PHYSICS MODEL
Before use: For a shaft that also carries bending or transverse shear: use a combined-stress check (e.g. von Mises) and a fatigue check, not this tool alone.
Validity: Solid round shaft (sizing) or concentric hollow round shaft (check), elastic pure torsion
Assumptions: Torsional stress from a given torque only. Bending, axial load and transverse shear from a gear/pulley/sprocket are not included — for most shafts that combined loading governs, not pure torsion alone. Also no stress concentration at keyways/shoulders/holes, no fatigue, and no stiffness (twist angle, deflection, critical speed). The 1.0/1.2 reserve band is a Mechify screening threshold, not a fixed code value.
Source details
τ = Tr/J; J = π(Dₒ⁴−Dᵢ⁴)/32 — Wiley / Philpot, Mechanics of Materials, ch. 6 · Verify
Checked 2026-10-08