Physics

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Pendulum Frequency Calculator.

Calculate ideal small-angle simple pendulum frequency.

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Set your values

Results update as you type.

Frequency: 0.498403 Hz

Frequency

0.498403Hz
Period: 2.006409 s

Period

2.006409s

Results update automatically as you type.

Use Cases

Physics homework and lab verification

Quickly compute the theoretical frequency of a simple pendulum for small oscillations, helping students verify experimental results or solve textbook problems.

Example: A 0.5 m pendulum on Earth (g=9.81 m/s²) has a frequency of about 0.704 Hz.

Designing pendulum-based timing devices

Estimate the frequency of a pendulum for clocks or metronomes, aiding in the selection of length to achieve a desired oscillation rate.

Example: To get a 1 Hz pendulum, set length to about 0.248 m on Earth.

Frequently Asked Questions

What is the pendulum frequency formula used by this calculator?
For small angles, the frequency is f = (1/(2π)) * sqrt(g/L), where g is gravity and L is the pendulum length. This calculator uses that formula to give the ideal frequency.
Why does the calculator specify 'small-angle'?
The formula assumes small angular displacements (typically less than about 15 degrees) where sin(θ) ≈ θ. For larger angles, the period becomes longer and the simple formula is less accurate.
What units should I use for length and gravity?
Enter the pendulum length in meters (m) and gravity in meters per second squared (m/s²). The calculator will output the frequency in hertz (Hz).

Tips & Common Mistakes

Tips

  • Ensure the pendulum length is measured from the pivot point to the center of mass of the bob.
  • Use the standard gravity value 9.81 m/s² for Earth unless you are on another planet or at a high altitude.
  • For small angles (less than 15°), the frequency is nearly independent of amplitude; this calculator assumes that ideal condition.
  • Double-check that your length is in meters; if you have centimeters, divide by 100 before entering.

Common Mistakes to Avoid

  • Using the diameter or radius of the bob as the length instead of the full length from pivot to center of mass.
  • Forgetting to convert length to meters, leading to incorrect frequency values.
  • Applying the formula to large-angle oscillations where the small-angle approximation is not valid.

Last updated: August 13, 2026