Shaft Size Calculator

A rotating shaft transfers power by carrying torque between a driver and a load. The torque depends on both power and speed: for power in kilowatts and speed in revolutions per minute, T = 9550 P / n gives torque in newton metres. Slow shafts must carry more torque than fast shafts transmitting the same power, which is why low-speed drive components are often visibly larger. This calculator sizes a solid circular shaft under ideal pure torsion. Maximum shear stress in such a shaft is tau = 16 T / (pi d cubed). Rearranging this relation and applying the entered safety factor gives the minimum diameter. Torque is converted from newton metres to newton millimetres so that allowable stress in megapascals, equivalent to newtons per square millimetre, produces a diameter directly in millimetres. Allowable shear stress should represent a defensible design limit for the selected material and service. It may come from a code, company standard, material test, or a fraction of yield strength. The safety factor increases the design torque to account for uncertainty, overloads, wear, and consequences of failure. Avoid counting the factor twice: if your allowable stress has already been reduced by a safety factor, enter 1 unless your design method specifically requires another multiplier. The result is a theoretical minimum for a smooth, solid, round shaft experiencing steady torque. Real shafts frequently include keyways, shoulders, splines, cross holes, threads, or retaining-ring grooves. These features create stress concentrations and can reduce fatigue strength. Belt pulls, gear forces, shaft weight, and misalignment also create bending stresses that pure torsion does not capture. Shock loads and reversing loads require fatigue and dynamic analysis. Choose the next suitable standard diameter above the calculated minimum, then verify deflection, angle of twist, critical speed, bearing fit, fatigue, and manufacturing tolerances. Hollow shafts require a different polar section equation and can save weight while preserving torsional stiffness. The calculator is best used for preliminary design, comparisons, coursework, and checking a detailed calculation, not as a substitute for applicable mechanical design standards or professional review.