What design criteria does this calculator use?

For a solid circular shaft with allowable normal stress Sa = Sy/N, von Mises uses d³ = 32/(πSa) × √[(KbM)² + 0.75(KtT)²]. Tresca uses d³ = 32/(πSa) × √[(KbM)² + (KtT)²], so it is the more conservative of the two.

What are typical values for stress concentration factors Kb and Kt?

For a smooth polished shaft with no features, Kb = Kt = 1.0. For a shaft with a keyway, Kb ≈ 1.3–2.0 and Kt ≈ 1.5–3.0. For sharp fillets or holes, values can exceed 2.5. Refer to your material and geometry data for precise values.

What safety factor should I use?

A safety factor of 1.5 to 2.0 is common for well-known, steady loads. Use 2.0 to 3.0 when loads are uncertain or variable. Critical applications in aerospace or safety-critical systems may require higher factors.

Are the results conservative?

The Tresca criterion is more conservative (larger diameter) than von Mises. Both assume solid round shafts. For hollow shafts, a separate calculation is needed. Always validate results with detailed fatigue analysis for production designs.

What units does the calculator accept?

Bending moment and torque are entered in N·m (Newton-meters), and yield strength in MPa (megapascals). Results are shown in millimeters (mm) and converted to inches for reference.

Shaft Diameter Calculator

Enter torque, bending moment, and material yield strength to get the minimum required shaft diameter using ASME design criteria.

Shaft Loads & Material

Bending Moment, M (N·m)

Torsional Moment, T (N·m)

Material Yield Strength, S_y (MPa)

Steel 1045: ~450 MPa • Mild steel: ~250 MPa • 4340: ~470 MPa

Safety Factor, N

K_b (bending SCF)

K_t (torsion SCF)

SCF = stress concentration factor. Use 1.0 for smooth shafts; higher for keyways or fillets.

Design Criterion

Von Mises (ASME) Tresca (Max Shear)

Enter loads and click Calculate to see the minimum shaft diameter.

Summary

This tool computes the minimum required shaft diameter for a rotating shaft subjected to combined torsion and bending loads. It applies either the ASME distortion energy criterion (von Mises) or the maximum shear stress (Tresca) criterion, accounting for a user-defined safety factor and fatigue stress concentration factors. Results are given in both millimeters and inches.

How it works

Enter the applied bending moment (M) and torsional moment (T) in N·m.
Provide the material yield strength (Sy) in MPa.
Set the desired safety factor (typically 1.5–3 for rotating shafts).
Optionally enter fatigue stress concentration factors for bending (Kb) and torsion (Kt).
Select the design criterion: ASME von Mises or Maximum Shear Stress (Tresca).
Click Calculate to see the minimum shaft diameter in mm and inches.

Use cases

Sizing motor output shafts and drive shafts in machinery.
Checking existing shaft designs against ASME standards.
Preliminary shaft sizing during mechanical system design.
Educational demonstration of combined-load shaft design equations.
Comparing von Mises vs. Tresca failure criteria on a real design.
Accounting for stress concentration factors at keyways and fillets.
Converting shaft dimensions between metric and imperial units.
Rapid design iterations when exploring different materials.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu