Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

Gravity Meters Per Second Squared (m/s²)

Required number input.

Static Deflection Meters (m)

Required number input.

Undamped first critical rotational speed estimated from a measured static shaft deflection under gravity: n=30√(g/δ)/π. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Critical Rpm (rpm)

The resulting critical rpm returned as a number.

• A basic critical-speed estimate idealizes shaft stiffness, support conditions, mass distribution, gyroscopic effects, damping, and bearing dynamics. Multi-mode rotor analysis and operating run-up or coast-down behavior may be required.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Motor Torque From Power

  Shaft torque from mechanical shaft power and rotational speed: T=P/(2πn/60).

• Beam Deflection Cantilever Point

  Free-end deflection of an ideal prismatic cantilever under a point force at the free end, neglecting shear deformation.

• Bevel Gear Pitch Angle

  Pitch cone angle of the first straight bevel gear in a 90° intersecting-shaft pair: atan(z1/z2).