Shaft Design Calculator: Diameter for Bending and Torque, Stress Check, Twist and Critical Speed

Size a power transmission shaft and check its stress and critical speed.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose to find the diameter or to check one. Enter the bending moment and the torque.

Pick the material and the factor of safety, with the shock factors if the load is not steady.

Enter the bearing span, the central mass and the running speed for the twist and critical speed checks.

Formulas used

  • d = \left(\frac{16\sqrt{(K_bM)^2 + (K_tT)^2}}{\pi\tau_{all}}\right)^{1/3}
  • \sigma_{vm} = \sqrt{\sigma^2 + 3\tau^2}
  • \theta = \frac{TL}{GJ}
  • n_c = \frac{60}{2\pi}\sqrt{\frac{g}{\delta}}

Worked example

With the default numbers in the calculator above:

  1. Allowable shear stress from the maximum shear stress theory: half the yield stress divided by the factor of safety: 41.667 MPa
  2. Equivalent twisting moment with the shock factors: 336.34 N m
  3. Minimum shaft diameter: 34.513 mm
  4. Next standard diameter above that: 35 mm (a keyway needs extra margin, so go up one size if the shaft is keyed)
  5. Bending stress and torsional shear stress at the surface (diameter 35 mm): 35.636 MPa bending and 29.697 MPa shear
  6. Von Mises equivalent stress: 62.575 MPa
  7. Factor of safety against yield (with no shock factors): 3.995
  8. Angle of twist between the bearings (shear modulus of steel 79.3 GPa): 0.613 degrees
  9. Deflection of the shaft under the central mass: 0.03467 mm
  10. First critical speed for that central mass (shaft mass ignored, simply supported): 5078.8 rev/min
  11. Running speed as a fraction of the critical speed: 0.197

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

How do I size a shaft?

Find the bending moment and torque at the critical section, combine them into an equivalent torque, and find the diameter that keeps the shear stress below the allowable value.

What is a critical speed?

A speed at which the shaft's natural frequency matches the rotation and it whirls. Keep the running speed well away from it.

Does this include fatigue?

Not directly. Use the shock factors and a generous factor of safety, and check keyways and shoulders separately.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any machine design text (shaft design by the maximum shear stress theory).

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