Shaft Diameter Calculator (Torsion & Bending)
Minimum solid shaft diameter for a transmitted power and speed from allowable shear stress — pure torsion and the ASME combined torsion-plus-bending equivalent — with actual stress, angle of twist and hollow-shaft option.
How it works
T = P ÷ ω = 9,549 × kW ÷ rpm; torsion: d = ∛(16 T ÷ (π τ)); ASME: d = ∛(16 ÷ (π τ) × √((Km M)² + (Kt T)²)); twist θ = T L ÷ (G J), J = π d⁴/32
A transmission shaft must carry its torque without excessive shear stress or twist, and at gear and pulley positions it also bends under radial loads. Pure torsion gives the classic cube-root relationship — diameter grows only with the cube root of torque, so doubling torque needs 26% more diameter — while the ASME code equation combines bending and torsion into an equivalent moment and applies shock factors for fluctuating loads. Allowable stress is conservative (40–55 MPa for ordinary steel with keyways) precisely because shafts fail in fatigue at stress raisers, not in a single overload. Once a standard diameter is chosen, the angle of twist is checked against rigidity limits, and for high-speed shafts the critical (whirling) speed and bearing deflections must be verified separately.
Worked example
15 kW at 1,450 rpm is 98.8 N·m of torque. With 120 N·m of bending and shock factors of 1.5, the equivalent moment is 233 N·m and at 40 MPa allowable the shaft needs 31 mm — use 35 mm, which twists 0.19° per metre.
Frequently asked questions
Solid or hollow?
Material near the centre carries little torque; a hollow shaft with 60% bore is about 8% larger for the same strength but 30% lighter — used where weight or a through-bore matters.
What allowable stress for a specific steel?
ASME B106.1: τ = 0.30 × yield or 0.18 × ultimate, whichever is smaller, reduced 25% at keyways. For C45/1045 normalised (Sy ≈ 310 MPa) that gives about 93 MPa, 70 MPa with a keyway.
Related calculators
Engineering estimate for education and preliminary design. Use manufacturer data, applicable standards and appropriate safety factors, and have critical designs checked by a qualified engineer.