Find the period of a simple pendulum from its length, or the reverse.
Calculated locally in your browser.
How do you calculate the period of a pendulum?
Period T = 2π · √(L ÷ g), where L is length in metres and g ≈ 9.81 m/s² on Earth. Rearranged, length L = g · (T ÷ 2π)², and frequency is 1 ÷ T. For example, a 1-metre pendulum has a period of about 2.01 seconds and a frequency near 0.50 Hz.
Understanding your result
For small swings, a simple pendulum's period depends only on its length and gravity — not on the mass of the bob or how far it swings. This is why pendulums make good timekeepers. At larger amplitudes the real period is slightly longer than this ideal formula predicts.
Formula and method
Period T = 2π · √(L ÷ g). Rearranged, length L = g · (T ÷ 2π)². Frequency is 1 ÷ T. On Earth, g ≈ 9.81 m/s².
Worked example
A 1-metre pendulum on Earth has a period of 2π·√(1 ÷ 9.81) ≈ 2.01 seconds and a frequency of about 0.50 Hz.
How to use this tool
- Choose whether you know the length or the period.
- Enter the value and, if needed, the gravity.
- Read the period, frequency and swings per minute.
Common mistakes to avoid
- Thinking a heavier bob changes the period — it does not.
- Using centimetres for length instead of metres.
- Applying the formula to very large swings, where it is only approximate.
About the Pendulum Calculator
The Pendulum Calculator finds the period and frequency of a simple pendulum from its length, or works out the length needed for a given period, using T = 2π·√(L ÷ g).
Who should use this tool
Physics students, teachers, clockmakers and hobbyists.
Benefits
- Period and frequency from length, or length from period.
- Adjustable gravity for other planets or precision.
- Shows swings per minute too.
- Private — calculated entirely in your browser.
Practical use cases
- Designing a pendulum for a one-second swing.
- Predicting how a longer pendulum swings more slowly.
- Checking physics homework.
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Frequently asked questions
Does mass affect the pendulum period?
No. For a simple pendulum with small swings, the period depends only on the length and gravity, not the mass.
What length gives a one-second period?
About 0.25 m on Earth. Use the period-to-length mode and enter 1 second to confirm.
Why is the formula only for small swings?
The simple formula assumes a small angle. At larger amplitudes the true period is a little longer.