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Shaft Diameter Design

⚙️ Mechanical · Required shaft diameter under bending + torsion (von Mises / DE-ASME criterion)

🧮 Calculate∑ Formula✅ Verification📚 Sources

Torque T (N·m)

Bending Moment M (N·m)

Yield Strength Sy (MPa)

Safety Factor n

🧱 Fill from Material (optional)

Selected Standard Diameter — for checking (mm)

Uncertainty mode (Monte Carlo, n=10,000)

Required minimum diameter d23.18 mm

Equivalent stress at selected diameter σ'54.43 MPa

Actual safety at selected diameter6.89

Status✅ Adequate

d = [ (32n / πSy) · √(M² + ¾T²) ]^⅓ — static load, distortion-energy (von Mises) criterion

💡 For dynamic/fatigue loading, notch factors and strength corrections (Marin factors) must also be applied; this tool is for static preliminary sizing.

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d = \left[\frac{32n}{\pi S_y}\sqrt{M^2+\tfrac{3}{4}T^2}\right]^{1/3}

Power-transmitting shafts (gearboxes, pump shafts, motor shafts) are almost always under the combined effect of bending and torsion — the force from a gear applies both a bending moment and a torsional moment to the shaft. Checking these two stress components separately is insufficient; the combined (equivalent) stress must be calculated.

This tool uses the DE-ASME static shaft design equation, based on the distortion-energy (von Mises) failure criterion. This approach is slightly less conservative than the maximum-shear-stress (Tresca) criterion and agrees better with experimental data for ductile materials.

Important limitation: this tool is for static loading only. The vast majority of real shaft applications are subject to cyclic (fatigue) loading — in that case, additional Marin factors such as notch factors (Kf), surface-finish correction, and size factor must be applied, and checked against the Soderberg or Goodman criteria. This tool is only a starting point for preliminary sizing.

📖 Sourced Formula · Single Verification

This tool's formula is based on a reliable source (see the Sources tab below) and has been checked against a hand-computed numerical example. A second, independent literature cross-check has not yet been added. As with any engineering calculation, we recommend independently confirming results before relying on them for critical decisions.

[1] Budynas, Richard G. and Nisbett, J. Keith. Shigley's Mechanical Engineering Design, 11 ed.. McGraw-Hill, 2020. ↗

Shaft Diameter Design — EngineersLab calc card

Formula: d = [(32n/πSy)·√(M²+¾T²)]^(1/3)

Sources: [1] Shigley's Mechanical Engineering Design

Tool version: 1.1.0 · Date:

Source URL: https://engineerslab.com.tr/en/araclar/mil

Results are for educational and preliminary-sizing purposes; final engineering design decisions must reference the relevant standards and a licensed engineer's approval.