Beam Natural Frequency Calculator
Calculate the first four Euler–Bernoulli bending frequencies for a uniform slender beam with ideal end conditions.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the standard ideal-support characteristic roots and a uniform Euler–Bernoulli bending model.
fn=βn²/(2πL²)×√(EI/(ρA))
Worked example
For pinned ends the frequency ratios are 1,4,9,16 because βn=nπ. Doubling beam length quarters every modeled frequency.
Assumptions and input details
Uniform straight slender beam, small bending, no attached masses, axial force, shear/rotary inertia or damping. Require L/√(I/A)≥20 for this scoped approximation. Ideal supports do not establish actual structural vibration or resonance safety.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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