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. This follows directly from Newton's second law applied to simple harmonic motion.

What units should I use for the spring constant?

Enter k in Newtons per meter (N/m). If you have it in kN/m, multiply by 1000 first. If you have lb/in, multiply by 175.127 to convert to N/m.

What is angular frequency and how does it differ from natural frequency?

Natural frequency f (Hz) counts full cycles per second. Angular frequency ω (rad/s) measures the same oscillation in radians: ω = 2πf. Engineers often work with ω in control system equations.

Does this account for damping?

No. This calculator is for undamped (ideal) spring-mass systems. In a damped system, the actual oscillation frequency is slightly lower: f_d = f × √(1 − ζ²), where ζ is the damping ratio. For light damping (ζ < 0.1) the difference is less than 0.5%.

What is the period and how is it related to frequency?

The period T is the time for one complete oscillation, measured in seconds. It is the reciprocal of frequency: T = 1 / f. A system oscillating at 2 Hz has a period of 0.5 s.

Can I use this for springs in series or parallel?

Yes — first compute the equivalent spring constant. Springs in series: 1/k_eq = 1/k1 + 1/k2. Springs in parallel: k_eq = k1 + k2. Then enter k_eq into this calculator.

Spring Frequency Calculator

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

Spring-Mass Inputs

Spring Constant (k)

N/m

Mass (m)

Formula

f = (1 / 2π) × √(k / m)

ω = 2π × f

T = 1 / f

Results

Enter k and m above to see results

Summary

This tool computes the natural frequency of an ideal spring-mass system using the formula f = (1/2π) * sqrt(k/m), where k is the spring constant in N/m and m is the mass in kilograms. It also outputs angular frequency (ω = 2πf) and the oscillation period (T = 1/f). All calculations run entirely in your browser — no data is sent to any server.

How it works

Enter the spring constant (k) in Newtons per meter (N/m).
Enter the mass (m) attached to the spring in kilograms (kg).
The calculator applies f = (1/2π) × √(k/m) to find the natural frequency.
Angular frequency ω = 2πf and period T = 1/f are derived automatically.
Results update instantly as you type — no button press required.

Use cases

Verify natural frequency in mechanical engineering design projects.
Study simple harmonic motion in physics coursework.
Check resonance frequency when designing vibration isolation systems.
Analyze suspension systems and damper spring combinations.
Quickly compare how changing stiffness or mass shifts the frequency.
Validate hand calculations during lab experiments.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu