Shaft Diameter Calculator

The minimum shaft diameter to carry a given torque — and bending, if any — without overstressing it. ASME method with shock and fatigue factors, from torque directly or from transmitted power and speed.

Units

Torque from

Torque T (in-lb)

Bending moment M (in-lb)

Allowable shear stress (psi)

Loading (ASME shock factors)

Minimum shaft diameter—

Sizing a Shaft for What It Carries

A power-transmission shaft has to twist without yielding and, usually, bend a little without overstressing. Too thin and it fails in torsion or fatigue; too thick and you waste material, weight and bearing cost. The ASME shaft equation combines the twisting and bending into one required diameter.

d³ = (16 / πτ) · √[ (K_mM)² + (K_tT)² ]

T is the torque, M the bending moment, τ the allowable shear stress, and K_m, K_t are factors that account for shock and fatigue. With no bending and steady load it reduces to the familiar pure-torsion result, d³ = 16T / πτ.

Torque From Power

If you know the power and speed instead of the torque, the shaft sees T = 63,025 × HP / RPM in inch-pounds (or T = 9,549 × kW / RPM in newton-metres). A slow shaft carrying the same power sees far more torque — which is why low-speed drives need fat shafts.

Shock Factors and Allowable Stress

A smoothly loaded, steadily rotating shaft uses K_m = 1.5 and K_t = 1.0; minor and heavy shock push both higher, reflecting the extra stress from sudden or reversing loads. The allowable shear is conservative — about 30% of yield or 18% of ultimate, and reduced roughly a quarter where a keyway cuts into the shaft.

Frequently Asked Questions

What if there is no bending?

Set the bending moment to zero and the equation gives the pure-torsion diameter. Short shafts between close bearings are often torsion-dominated; long or side-loaded shafts are not.

Why round the diameter up?

The result is a minimum. Round up to standard stock and to a size that matches your bearings, couplings and keyseats – and re-check stress concentrations at any shoulder or keyway.

Does this include fatigue?

Only through the shock factors. A full fatigue design uses endurance limit, stress-concentration factors and a Soderberg or Goodman check – beyond this preliminary sizing.

Related calculators

Torque Calculator — the torque the shaft must carry.
Gear Ratio Calculator — how the drive changes torque and speed.
Belt Length Calculator — the other half of a pulley drive.
Mechanical Stress Calculator — general stress and safety factor.

For education and preliminary sizing only. Shaft design must address fatigue, stress concentrations, deflection, critical speed and bearing loads per the applicable standard, and be performed by a qualified engineer.