Physics
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Pendulum Frequency Calculator.
Calculate ideal small-angle simple pendulum frequency.
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Results update as you type.
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