TorqueMath

Shaft Diameter Calculator

Find the smallest safe diameter for a rotating shaft that carries torque and a belt, chain or gear load. Checks strength (ASME code with shock factors and keyway), twist and deflection, then picks the next standard size.

kW
rpm
Load layout
kN
V-belt ≈ 2 × belt pull, chain ≈ 1.2 ×, spur gear ≈ 1.1 × tangential force. 0 = torque only.
mm
mm
Material
Load type (shock factors)
° per m
0.25 °/m for machine shafts, 1 °/m for general line shafts, 3 °/m when stiffness hardly matters.
Shaft between bearings

Standard sizes for this case

DiameterMax power by strengthSafety factorTwistDeflection

How it is calculated

Strength follows the ASME code for transmission shafts: a combined bending and torsion check with shock factors and a 25% strength cut for a keyway. Then the twist limit is checked, and the deflection at the load is calculated for the chosen standard diameter.

Torque T = 9549 · P / n N·m Bending moment between bearings M = F·a·(L−a)/L, overhung M = F·a Allowed shear τall = min(0.30·Sy, 0.18·Su) × 0.75 with keyway Strength d = ( 16 / (π·τall) · √((Km·M)² + (Kt·T)²) )^(1/3) Twist d = ( 32·T / (π·G·θ) )^(1/4) θ in rad/mm Von Mises σv = √(σb² + 3τ²), σb = 32M/(πd³), τ = 16T/(πd³) Deflection between: y = F·a²·b² / (3·E·I·L), overhung: y = F·a²·(L+a) / (3·E·I)

Shock factors (ASME, rotating shafts): steady load Km 1.5 / Kt 1.0, minor shock 2.0 / 1.5, heavy shock 3.0 / 3.0. Material values are typical minimums for 16 – 40 mm bar. Check your supplier's certificate. Keep deflection under span/2000 for gear shafts and the bearing slope under 0.001 rad for ball bearings. This is a first sizing. Fatigue at shoulders and grooves needs its own check with the real notch factors.

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