Beam Natural Frequency Calculator
First and second natural frequencies of a simply supported beam, with the static deflection and the deflection-based estimate.
Results
Natural frequency
11.5443
Hz
Natural frequency
46.1771
Hz
Time
0.08662
s
Deflection
2.3641
mm
Natural frequency
11.5174
Hz
What this tool does
Frequency falls with the square of the span, so a beam twice as long vibrates at a quarter the frequency — and that is what brings long floors down into the range people excite by walking, roughly 1.5 to 2.5 Hz for the pace and up to 8 Hz for the harmonics. Design guidance commonly asks for a first mode above about 8 Hz for ordinary floors, and higher where equipment is sensitive.
Formula
f₁ = (π ÷ 2L²) √(E I ÷ m) (simply supported beam)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
em | Young's modulus | GPa |
iy | Second moment of area | cm⁴ |
lb | Span | m |
ml | Mass per metre | kg/m |
F1 | Natural frequency | Hz |
F2 | Natural frequency | Hz |
PR | Time | s |
DF | Deflection | mm |
FC | Natural frequency | Hz |
Worked example
- Young's modulus210 GPa
- Second moment of area2000 cm⁴
- Span6 m
- Mass per metre60 kg/m
- Natural frequency11.5443 Hz
- Natural frequency46.1771 Hz
- Time0.08662 s
- Deflection2.3641 mm
- Natural frequency11.5174 Hz
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.