A pendulum is a weight hanging from a pivot, swinging back and forth under gravity. Its period is the time for one complete swing, out and back. The surprising fact, found by Galileo, is that for small swings the period depends almost only on the length of the pendulum and on gravity. It does not depend on the weight of the bob, and it does not depend much on how far it swings, as long as the swing stays small. That is why pendulum clocks can keep steady time.
The formula is T = 2π√(L/g). Here T is the period in seconds, L is the length in metres from the pivot to the centre of the bob, and g is gravity in metres per second squared. On Earth g is about 9.81. A pendulum one metre long has a period of about 2.01 seconds, which means it takes about one second to swing each way. Clock makers used this: a seconds pendulum, with a two-second period, is about 0.994 metres long, close to one metre.
Here is a worked example. Take a pendulum 0.25 metres long, like a short classroom demo. Divide length by gravity: 0.25 divided by 9.81 is about 0.0255. The square root of that is about 0.160. Multiply by 2π, about 6.283, and you get a period of about 1.00 second. So a quarter-metre pendulum swings once per second. Halving the length does not halve the period: because of the square root, a pendulum must be four times shorter to swing twice as fast.
Frequency is the flip side of period. It counts swings per second and is measured in hertz. Frequency equals one divided by the period, so our one-metre pendulum, with a period near 2 seconds, has a frequency near 0.5 hertz, or about 30 swings per minute. Short pendulums tick fast and long pendulums tick slowly. That is why a grandfather clock, with a long pendulum near one metre, ticks about once per second, while a tiny metronome pendulum ticks much faster.
Gravity changes the answer, and this tool lets you try other worlds. On the Moon, where gravity is only 1.62, a one-metre pendulum has a period of about 4.94 seconds, more than twice as slow as on Earth. On Jupiter, with gravity near 24.8, the same pendulum would swing in about 1.26 seconds. This is not just a curiosity: it shows that a pendulum clock carried to the Moon would run slow, and it gives a neat way to measure gravity by timing swings.
The formula has clear limits, and they matter for real pendulums. It assumes small swings, usually under about 15 degrees, a massless string, and a small heavy bob. At large angles the period grows longer than the formula says, by about 2 percent at 30 degrees and much more beyond that. Air resistance slowly steals energy, so a real pendulum needs a push or a clock drive to keep going. A heavy rod or a large bob also shifts the effective length.
Pendulums appear in more places than clocks. Playground swings follow the same rule, which is why a longer swing chain gives a slower, lazier ride. Seismometers use pendulums to sense ground motion, and old buildings sometimes hang tuned mass dampers, giant pendulums that sway against the wind. Even a child on a swing can test the rule: time ten swings, divide by ten, and compare with the formula for the chain length.
To use this tool well, measure length carefully, from the pivot point to the centre of the bob, not to its top or bottom. Time ten full swings with a stopwatch and divide by ten, rather than timing one swing, because reaction time matters less over ten swings. Keep the swing small, under about 15 degrees, and repeat the timing twice. If your measured period differs from the tool by more than a few percent, check the length measurement first, since it is the usual culprit.