Pendulum Calculator
Find the period and frequency of a simple pendulum.
Results update as you type.
How it works
A simple pendulum is a mass swinging on a string, and this calculator finds how long each swing takes and how many swings happen per second. You enter the length of the pendulum, with gravity defaulting to Earth's value, and it returns the period and the frequency. One of the most surprising results in physics is that the period depends only on the length and the strength of gravity, not on the mass of the bob or, for small swings, on how far it swings. Lengthen the pendulum and it swings more slowly; the period grows with the square root of length, so making a pendulum four times longer doubles its period. This principle made pendulums the heart of accurate clocks for centuries, since a fixed length gives a fixed, reliable beat. It is also used to measure the local acceleration of gravity, to demonstrate simple harmonic motion in classrooms, and in seismometers and metronomes. Changing the gravity value lets you model a pendulum on the Moon or another planet, where weaker gravity makes it swing more slowly. The formula assumes small swing angles and an ideal, frictionless setup. Enter the length to find the period and frequency.
T = 2π · √(L / g)
The period of a simple pendulum, the time for one complete swing back and forth, equals two pi times the square root of the length divided by the gravitational acceleration. Notably, the period does not depend on the mass of the bob or, for small swings, on the amplitude. The frequency, the number of swings per second, is simply the reciprocal of the period.
Source:Classical mechanics (simple pendulum)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter pendulum length.
- 2
Adjust the options
Adjust gravity (optional) if they apply — sensible defaults are already set.
- 3
Read your result
Period updates instantly as you type — no button to press.
Frequently asked questions
What determines a pendulum's period?
For a simple pendulum with small swings, the period depends only on the length of the pendulum and the local acceleration of gravity. A longer pendulum swings more slowly, and stronger gravity makes it swing faster. Remarkably, the mass of the bob and the swing amplitude do not affect the period, as long as the angle stays small.
Does the mass of the bob matter?
No. For an ideal simple pendulum, the period is completely independent of the mass hanging on the string. A heavy bob and a light bob of the same string length swing with exactly the same period. This is because gravity accelerates all masses equally, so the mass cancels out of the equation of motion.
Why is the pendulum used in clocks?
Because a pendulum of fixed length swings with a fixed, regular period, it provides a steady timekeeping beat. Pendulum clocks, invented in the seventeenth century, were the most accurate timekeepers for nearly three hundred years. Adjusting the pendulum's length slightly speeds up or slows down the clock, which is how such clocks are regulated.
Does amplitude affect the period?
For small swings, no; the period is essentially constant regardless of amplitude, a property called isochronism that makes pendulums good timekeepers. However, for large swings beyond about fifteen degrees, the period increases slightly with amplitude and the simple formula becomes less accurate. This calculator assumes the small-angle approximation, which covers most practical situations.
Can I use it for other planets?
Yes. Change the gravity value to match another body: about 1.62 metres per second squared for the Moon or 3.72 for Mars. Weaker gravity makes the pendulum swing more slowly, lengthening the period, while stronger gravity shortens it. This lets you explore how the same pendulum would behave under different gravitational conditions.