Calculate minimum shaft diameter from torque or power/RPM with shock factors, hollow shaft support, and material comparison table.
Shaft sizing is a fundamental mechanical engineering task. A shaft must be large enough to transmit the required torque without exceeding the allowable shear stress of its material, yet not so large as to be wastefully heavy. The basic approach derives the minimum diameter from the torsion formula, modified by shock and fatigue factors.
For power transmission, torque is calculated from power and rotational speed: T = P × 60 / (2πN). The ASME code introduces combined shock and fatigue factors Km and Kt that increase the design torque to account for real-world loading conditions — from steady loads in constant-speed drives to heavy shock in rolling mills and crushers.
Hollow shafts save weight while maintaining stiffness. A shaft with inner-to-outer diameter ratio of 0.6 saves about 36% of weight while retaining 87% of the torsional strength of an equivalent solid shaft. This calculator sizes both solid and hollow shafts, recommends standard sizes, and checks angular deflection limits.
Use this when you need a first-pass shaft diameter from torque, power, or RPM. It is helpful for machine design, drive trains, and repairs where you need to choose a standard size quickly before doing a full combined-load check.
Minimum shaft diameter: d = (16T_d / πτ)^(1/3), where T_d = K_t × T (design torque with shock factor), τ = allowable shear stress. For hollow shafts, multiply by 1/(1 − k⁴)^(1/3) where k = dᵢ/dₒ. Torque from power: T = P × 60 / (2πN).
Result: 20 mm recommended
At 10 HP (7457 W) and 1800 RPM, torque is 39.6 N·m. With Kt=1.0 (light shock), the minimum solid diameter is about 16.5 mm. The next standard size is 17 mm (or 20 mm for extra margin).
The diameter output is the minimum size that keeps the calculated torsional shear stress within the value you entered. It does not automatically include bending, keyway weakening, or fatigue beyond the selected load factor.
Hollow shafts are useful when weight matters or when the center of the shaft needs to carry wiring or fluid. A hollow shaft can be lighter while still providing much of the torsional stiffness of a solid section.
After you get the calculated size, compare it with the next standard shaft size and then check deflection, keyway effects, and bearing fits before finalizing the design.
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For mild steel, 40 MPa is conservative. For alloy steel (4140, 4340), 55-80 MPa is common. Use 0.3 × yield strength or 0.18 × ultimate as a guideline.
Km and Kt account for bending and torsional shock. Steady loads: 1.0/1.0. Minor shock: 1.5/1.0. Moderate shock: 1.5/1.5. Heavy shock: 2.0/1.5.
When weight reduction is important (rotating equipment, vehicles) or when a bore is needed (hydraulic lines, wiring). Hollow shafts have higher critical speeds for the same weight.
A standard keyway reduces torsional strength by about 25%. Multiply the required diameter by approximately 1.1 to compensate, or use the net section approach.
General machinery: 0.25°/m. Precision drives/machine tools: 0.08°/m. Excessive deflection causes gear misalignment and vibration.
This calculator is sized around torsion. If the shaft also carries bending, use the result as a starting point and then check combined stress with an equivalent torque or an ASME-style combined-load calculation.