Natural Frequency of a Beam Calculator

Summary

This calculator uses Euler-Bernoulli beam theory to compute the fundamental natural frequency of a uniform beam. Three common boundary conditions are supported: simply supported (pinned-pinned), cantilever (fixed-free), and fixed-fixed. Inputs are beam length, elastic modulus, second moment of area (moment of inertia), and linear mass density. All calculations run entirely in your browser — no data is sent to any server.

How it works

1. Select the boundary condition that matches your beam: simply supported, cantilever, or fixed-fixed.
2. Enter the beam length L in meters (m).
3. Enter the elastic modulus E in Pascals (Pa) — e.g., 200e9 for structural steel.
4. Enter the second moment of area I in m⁴ — e.g., from section tables or your own calculation.
5. Enter the linear mass density m (mass per unit length) in kg/m.
6. Click Calculate to see the fundamental natural frequency in Hz and the angular natural frequency in rad/s.

Use cases

• Checking whether a floor beam natural frequency exceeds the 8 Hz serviceability threshold.
• Designing machine support frames to avoid resonance with equipment operating frequencies.
• Estimating bridge girder natural frequencies for pedestrian loading assessment.
• Validating finite element modal analysis results against closed-form solutions.
• Teaching structural dynamics and Euler-Bernoulli beam vibration in engineering courses.
• Preliminary sizing of cantilever brackets to avoid resonance with pump or motor speeds.
• Comparing natural frequencies of different cross-sections or materials for beam selection.
• Checking that antenna masts or signpost poles will not resonate at wind vortex-shedding frequencies.

Frequently Asked Questions