Shaft Torque Calculator
Determine the minimum shaft diameter needed to safely transmit a given power at a specified speed and shear stress limit. Essential for mechanical designers sizing drive shafts, motor shafts, and spindles.
About this calculator
A shaft transmitting power experiences a twisting moment called torque T, calculated as T = P × 60 / (2π × n), where P is power in watts and n is speed in rpm. The resulting shear stress τ in a solid circular shaft is τ = 16T / (π × d³), derived from the torsion formula. Rearranging to find the minimum required diameter: d = ∛(16 × SF × T / (π × τ_allow)), where SF is the safety factor and τ_allow is the allowable shear stress. The calculator implements this directly: d = ∛(16 × SF × (P × 1000 × 60) / (2π × n) / (τ_allow × 10⁶ × π)). Larger safety factors or lower allowable stress values yield larger required diameters. This ensures the shaft will not yield or fracture under torsional loading.
How to use
Design a shaft for: Power = 15 kW, Speed = 960 rpm, Allowable shear stress = 40 MPa, Safety factor = 2. Step 1 — torque: T = (15,000 × 60) / (2π × 960) = 149.2 N·m. Step 2 — apply safety factor: T_design = 2 × 149.2 = 298.4 N·m. Step 3 — solve for diameter: d = ∛(16 × 298.4 / (π × 40 × 10⁶)) = ∛(4,774.4 / 125,663,706) = ∛(0.00003799) ≈ 0.0336 m = 33.6 mm. Round up to the next standard size (e.g., 35 mm). Enter your values above to calculate instantly.
Frequently asked questions
What safety factor should I use when designing a power transmission shaft?
Typical safety factors for solid steel shafts range from 1.5 to 3.0 depending on the application. A factor of 1.5–2.0 is common for steady, well-characterised loads in controlled environments such as machine tools. Factors of 2.0–3.0 are used where shock loads, vibration, stress concentrations at keyways or shoulders, or uncertainty in material properties exist. For safety-critical applications such as vehicle drive shafts or lifting equipment, higher factors and full fatigue analysis are recommended.
How does shaft speed affect the required shaft diameter for a given power?
Higher shaft speed reduces the torque required to transmit the same power, because T = P / ω and angular velocity ω increases with speed. Lower torque means a smaller shaft diameter can be used, which is why high-speed gearbox output shafts are smaller than low-speed ones transmitting identical power. This is a key reason for using speed-increasing gearboxes: smaller, lighter shafts become feasible. However, high-speed shafts introduce dynamic considerations such as critical speed and bearing DN values that must also be checked.
What is the difference between allowable shear stress and tensile strength for shaft design?
Tensile strength refers to the maximum axial stress a material can withstand before fracture, while allowable shear stress is the permissible torsional shear stress used in shaft design, typically 0.3–0.5 times the tensile yield strength per various design codes. Shafts primarily experience torsion and bending, so shear stress is the governing criterion. The allowable value already incorporates factors for fatigue, surface finish, and stress concentration. Using the tensile strength directly without applying these reductions would result in an unsafe, undersized shaft.