Shaft Size Calculator

First calculate torque: T = (P × 60) / (2π × N) = (20,000 × 60) / (2π × 200) ≈ 955 N·m. Then apply the torsion formula: d = ∛(16T / (π × τ_allowable)). With an allowable shear stress of 40 MPa and a safety factor of 2 (effective stress 20 MPa), the minimum diameter works out to approximately 63 mm. You can verify this instantly using the calculator above.

A shaft is a rotating member that transmits torque and power — it rotates along with the components mounted on it. An axle, by contrast, is a stationary member that supports rotating components such as wheels. Because shafts transmit torque, they must be designed to resist torsional shear stress, whereas axles are primarily designed to resist bending.

Torsional yield strength is the maximum shear stress a material can withstand before permanent (plastic) deformation begins. It is typically estimated as 0.577 times the tensile yield strength (von Mises criterion). Shaft designers use this value — divided by a safety factor — as the allowable shear stress to ensure the shaft operates safely within its elastic range under the applied torque.

Camshafts require very precise angular positioning to control valve timing. Excessive torsional deflection (twist) along the shaft length can cause timing errors that reduce engine efficiency and increase emissions. For such applications, shaft size must be selected not only for stress limits but also for a maximum allowable angle of twist — typically expressed in degrees per metre of shaft length.

For solid steel transmission shafts, typical allowable shear stresses range from 40 MPa to 60 MPa for shafts without keyways, and 30–45 MPa for shafts with keyways (which introduce stress concentrations). Alloy steels such as AISI 4140 can sustain higher values. Always divide the material's torsional yield strength by an appropriate safety factor (usually 1.5–3) to determine the allowable design stress.

When a gearbox increases torque (speed reduction), the output shaft must carry a proportionally higher torque than the input shaft. If the same shaft diameter is used on both sides, the output shaft will have a lower safety factor. Proper shaft design accounts for the gear ratio so that each shaft section is appropriately sized for the torque it actually carries.

When a shaft experiences both bending moment (M) and torque (T), the equivalent torque method is used: T_eq = √(M² + T²). This equivalent torque is then substituted into the standard torsion formula to find the required diameter. The ASME code also introduces shock and fatigue factors (Km and Kt) to account for dynamic loading, yielding T_eq = √((Km·M)² + (Kt·T)²).

The calculator currently computes solid shaft diameters. For hollow shafts, the polar moment of inertia J = π(D⁴ − d⁴)/32 must be used instead of J = πD⁴/32. Hollow shafts offer a better strength-to-weight ratio and are preferred in applications where weight saving is critical, such as aerospace and marine driveshafts.