Pendulum Calculator
How long one swing of a pendulum takes — or how long the string must be for a given beat, or what gravity is where you are. Includes the exact correction for large swings and works on any planet.
How Does a Pendulum Work?
A pendulum is a weight on a string or rod that swings back and forth under gravity. The time for one full swing — there and back — is the period. Remarkably, it does not depend on the mass of the bob, and for small swings hardly on how far you pull it aside.
That is why pendulums kept the time in clocks for almost 300 years. A longer string swings more slowly; four times the length doubles the period. Stronger gravity makes it swing faster, so a pendulum can also be used to measure g.
Live Pendulum
real timePeriod and Amplitude
exactA 1 m Pendulum Elsewhere
small swings| Place | g (m/s²) | Period |
|---|---|---|
| Earth | 9.81 | 2.01 s |
| Moon | 1.62 | 4.94 s |
| Mars | 3.71 | 3.26 s |
| Jupiter (cloud tops) | 24.79 | 1.26 s |
Worked Techniques
Time 10 or 20 full swings with a stopwatch and divide: that spreads your reaction time over many swings. Keep the amplitude small.
A grandfather clock ticks once per second, so each one-way swing takes 1 s and the period is 2 s. That needs a pendulum just under a metre long.
The simple formula assumes small swings. For wide swings the period grows; this exact form uses the arithmetic–geometric mean and is what the calculator uses.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 15 (Oscillations).