Pendulum Calculator

This calculator finds the period and frequency of a simple pendulum from its length and the local strength of gravity. A simple pendulum, a mass swinging on a light string, is one of the most elegant systems in physics, and its behaviour holds a famous surprise: for small swings, the time it takes to complete one full back-and-forth, the period, depends only on the length of the string and gravity, not on the mass of the bob or how far it swings. This is why pendulums kept accurate time in clocks for centuries. The period is given by two pi times the square root of the length divided by gravitational acceleration. A longer pendulum swings more slowly, and the relationship is a square-root one, so to double the period you must quadruple the length. This tool makes exploring it easy. You enter the length in metres and, if you wish, adjust gravity from its standard value of about 9.81 metres per second squared, and the calculator returns the period in seconds. It also gives the frequency, the number of swings per second in hertz, and the number of complete swings per minute, which helps connect the physics to something you can picture. The results update as you type, so you can see how lengthening the pendulum stretches out each swing. Use it for physics homework, for designing a pendulum or metronome, or to understand simple harmonic motion. A note on accuracy: the formula assumes small swings and a rigid, massless string, which is an excellent approximation for modest angles but less exact for very wide swings. The results are rounded for display.

Valid for small swings of a simple pendulum. Period = 2 pi x square root of (length / gravity). Standard gravity is 9.81 m/s². Rounded for display.