Physics

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Natural Frequency Calculator.

Calculate undamped single-degree-of-freedom natural frequency.

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01

Set your values

Results update as you type.

Natural frequency: 3.558813 Hz

Natural frequency

0.000000Hz
Angular frequency: 22.36068 rad/s

Angular frequency

0.000000rad/s

Results update automatically as you type.

Use Cases

Mechanical System Design

Engineers use natural frequency to avoid resonance in structures and machines. This calculator helps quickly determine the fundamental frequency of a simple spring-mass system.

Example: A spring with stiffness 2000 N/m and a mass of 5 kg gives a natural frequency of about 3.18 Hz.

Educational Demonstrations

Physics students can verify theoretical predictions of oscillation frequency for a mass-spring setup, reinforcing concepts of simple harmonic motion.

Example: Check the frequency of a 0.5 kg mass on a spring with k=100 N/m.

Frequently Asked Questions

What is the natural frequency of a single-degree-of-freedom system?
The natural frequency is the rate at which a system oscillates when disturbed from equilibrium, without damping. For a spring-mass system, it depends on the spring stiffness (N/m) and mass (kg) and is calculated as the square root of stiffness divided by mass, divided by 2π.
How do I use this calculator?
Enter the spring stiffness in N/m and the mass in kg. The calculator will compute the undamped natural frequency in hertz (Hz) using the formula f = (1/2π)√(k/m). Ensure units are consistent.
What units does the calculator use?
The calculator expects spring stiffness in newtons per meter (N/m) and mass in kilograms (kg). The result is the natural frequency in hertz (Hz).

Tips & Common Mistakes

Tips

  • Ensure the mass is in kilograms and stiffness in N/m to get frequency in Hz.
  • This calculator assumes undamped conditions; real systems with damping will have slightly lower frequencies.
  • For a single-degree-of-freedom system, the natural frequency is independent of initial displacement or velocity.
  • Double-check your input values; small errors in stiffness or mass can significantly affect the result.

Common Mistakes to Avoid

  • Using grams instead of kilograms for mass, leading to incorrect frequency values.
  • Forgetting to convert stiffness from N/mm to N/m; 1 N/mm = 1000 N/m.
  • Confusing angular frequency (rad/s) with frequency (Hz); this calculator gives Hz.

Last updated: August 13, 2026