What is the formula used?

The natural frequency is f = (1 / (2π)) × √(k / m), where k is the spring constant in N/m and m is the mass in kg. Angular frequency ω = √(k/m) in rad/s. Period T = 1/f in seconds.

What units should I use for input?

Enter mass in kilograms (kg) and spring constant in newtons per meter (N/m). The output frequency is in hertz (Hz) and angular frequency in radians per second (rad/s).

What is the difference between Hz and rad/s?

Hertz (Hz) measures cycles per second — how many full oscillations occur each second. Radians per second (rad/s) is angular frequency; they are related by ω = 2πf.

Does damping affect the resonance frequency?

This calculator assumes an undamped system. In real systems with damping, the damped natural frequency is slightly lower: f_d = f × √(1 − ζ²), where ζ is the damping ratio. For most lightly-damped systems the difference is negligible.

Can I use this for a spring with no attached mass?

No — you need both a mass and a spring constant. A spring alone does not oscillate; it is the interaction of the restoring spring force and the inertia of the mass that creates resonance.

How do I find the spring constant of a real spring?

Measure the deflection δ (meters) when a known force F (newtons) is applied; then k = F / δ. Alternatively, hang a known mass, measure the static extension, and use k = mg / δ.

Resonance Frequency System

Enter mass and spring constant to instantly calculate the natural resonance frequency of a mass-spring system.

System Parameters

Mass (kg)

Mass of the object attached to the spring.

Spring Constant (N/m)

Stiffness of the spring in newtons per meter.

Enter mass and spring constant to see results.

Copied!

Summary

Enter mass and spring constant to instantly calculate the natural resonance frequency of a mass-spring system.

How it works

Enter the mass of the object attached to the spring in kilograms.
Enter the spring constant (stiffness) in newtons per meter (N/m).
The tool applies the formula f = (1/2π)√(k/m) to find natural frequency.
Angular frequency ω = √(k/m) is also calculated in radians per second.
Period T = 1/f shows the time for one complete oscillation cycle.
Click Calculate (or press Enter) after entering both values to update the results.

Use cases

Mechanical engineering design of vibration isolation systems.
Determining if a structure might resonate at a given excitation frequency.
Physics coursework and lab calculations for simple harmonic motion.
Automotive suspension spring selection and tuning.
MEMS sensor design — calculating resonant frequency of micro-cantilevers.
Earthquake engineering — estimating building natural frequencies.
Audio transducer and speaker suspension design.
Quick sanity checks during FEA (finite element analysis) modeling.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu