Pendulum Period Calculator
Calculate the period and frequency of a simple pendulum from its length and the acceleration due to gravity.
Last reviewed by the Radiatus Cloud team
Calculate the period of a simple pendulum from its length.
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Calculate a pendulum's period
A simple pendulum is a mass swinging on a light string, and its period, the time for one complete back-and-forth swing, depends only on its length and the acceleration due to gravity, not on the mass or, for small swings, the amplitude. The period equals two pi times the square root of the length divided by gravity. A one-metre pendulum on Earth has a period of about two seconds. The calculator also gives the frequency, the number of swings per second.
This surprising independence from mass is a classic result that makes pendulums reliable timekeepers.
Pendulums in science
The regular period of a pendulum made it the heart of accurate clocks for centuries and remains a staple demonstration in physics. Because the period depends on gravity, a pendulum can even be used to measure the local strength of gravity. The formula assumes small swings; for large amplitudes the motion is more complex and the period lengthens slightly.
A longer pendulum swings more slowly, which is why grandfather clocks have long pendulums tuned to a convenient period. Use a consistent gravity value for the location. All calculation happens locally in your browser.
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Frequently Asked Questions
What determines a pendulum\'s period?
For a simple pendulum with small swings, only its length and the acceleration due to gravity, not the mass or amplitude.
What is the pendulum period formula?
The period equals two pi times the square root of the length divided by the gravitational acceleration.
Why does mass not affect the period?
In the idealised simple pendulum, mass cancels out of the equation, so a heavy and a light bob of the same length swing at the same rate.
Does the swing size matter?
For small swings the period is nearly constant, but for large amplitudes the period increases slightly and the simple formula is only approximate.
How can a pendulum measure gravity?
Rearranging the formula, measuring the period and length lets you solve for the local gravitational acceleration.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter the pendulum length and gravity.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.