Critical Speed of a Shaft Calculator
Enter shaft geometry, material, and support conditions to compute the first critical (whirling) speed in RPM and Hz using Rayleigh's method or beam formulas.
Use the Critical Speed of a Shaft Calculator
Inputs
Enter each point mass and its static deflection under gravity. Use a beam deflection formula or enter measured/FEA values.
Fill in the inputs and click Calculate
First Critical Speed
Operating Speed Check
Calculation Details
Summary
This calculator computes the first critical (whirling) speed of a rotating shaft — the rotational speed at which the shaft resonates with its own transverse natural frequency. Two methods are available: a direct beam-formula approach for uniform simply supported or cantilever shafts (using Euler-Bernoulli theory), and Rayleigh's energy method for a shaft carrying one or more discrete point masses. All calculations run entirely in your browser.
How it works
- Select the calculation method: Beam Formula (uniform shaft) or Rayleigh's Method (shaft with point masses).
- For the Beam Formula method, enter shaft length, diameter, elastic modulus, and density; choose simply supported or cantilever support.
- For Rayleigh's Method, add each discrete mass with its corresponding static deflection under gravity.
- Click Calculate to see the first critical speed in RPM and Hz.
- Compare the result against the operating speed to confirm an adequate separation margin (typically ±20%).
Use cases
- Verifying that a motor shaft or pump shaft does not pass through resonance within the operating speed range.
- Preliminary sizing of drive shafts in industrial machinery and turbines.
- Checking overhung rotor configurations (cantilever) against whirling limits.
- Teaching rotor dynamics and critical speed theory in mechanical engineering courses.
- Estimating the effect of adding a disk or impeller mass on shaft critical speed.
- Comparing solid versus hollow shaft cross-sections for resonance avoidance.