Shaft Size Calculator

Determine the minimum diameter of your shaft using our shaft size calculator.

Minimum shaft diameter33.334 mm1.3124 inches — round UP to the next standard size

Design torque400 N·mpure torsion, no allowance for bending or shock

Allowable shear stress55 MPa55 MPa

Actual shear at that diameter55 MPaequal to the allowable, by construction

Polar second moment J1.212e-7 m⁴

Power transmitted60.7375 kW81.45 hp at 1,450 rpm

At twice the torque41.998 mmonly 26% larger — diameter goes as the cube root of torque

A 10% larger shaft carries1.331× the torquethe cube works the other way too, which is why rounding up to the next standard size buys a lot of margin cheaply

A hollow shaft of the same strengthsaves weight for the same Jmaterial near the axis contributes almost nothing to torsional strength, since the stress rises linearly with radius and is zero at the centre

The formula

d = ∛(16T ÷ πτ) for a solid round shaft in torsion

Stress is zero at the centre

Twisting a round shaft produces shear stress that rises linearly from zero at the axis to a maximum at the surface. The material near the centre is barely working, which is why a hollow shaft is so much more efficient by weight than a solid one of the same strength.

Maximum shear is 16T/πd³, so the required diameter goes as the cube root of torque. That makes shaft sizing unusually forgiving: doubling the torque needs only 26% more diameter, and rounding up to the next standard size typically buys a third more capacity for nothing.

The allowable stress is where the real engineering sits. It must account for the material, the stress concentration at keyways and shoulders — which can easily double the local stress — fatigue under reversing loads, and shock. Published design allowables for steel shafts with keyways are often around 40 MPa, far below the material's actual shear strength, for exactly these reasons. The combined-loading factor here is a crude stand-in for a proper bending-and-torsion analysis, not a substitute for one.