Vibration Natural Frequency Calculator

Formula

• ωn = √(k / m)
• fn = ωn / (2π)
• T = 1 / fn
• ζ = c / (2√(km))
• fd = fn × √(1 − ζ²) for underdamped

About this calculator

Part of our Mechanical Calculators collection. Beams, bolts, springs, gears, bearings, and core ME calculations.

How it works

Natural angular frequency is the square root of stiffness divided by mass. Natural frequency in Hz divides angular frequency by 2 pi. Damped mode adds damping ratio, critical damping, and damped natural frequency when c is greater than zero.

Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.

Worked example

Spring stiffness 5000 N/m, mass 2.5 kg, undamped model.

1. ωn = √(5000 / 2.5) = 44.72 rad/s
2. fn = 44.72 / 2π = 7.12 Hz
3. Period T = 0.140 s

Result: Natural frequency 7.12 Hz, undamped SDOF response.

When to use

• Estimating natural frequency of a spring-mass system
• Checking whether operating speed avoids resonance
• Quick damping ratio check for underdamped systems

Limitations

• Single degree of freedom only
• Damped mode uses viscous damping; structural damping not modeled
• Does not include support stiffness or multi-mass systems

FAQ

What damping states are shown?

Undamped (ζ = 0), underdamped (ζ < 1), critical (ζ = 1), and overdamped (ζ > 1) are labeled in the results.

When should I use damped mode?

Switch to viscous damping when you know the damping coefficient c and want damped natural frequency and damping ratio.