{"id":604,"date":"2026-07-17T22:18:27","date_gmt":"2026-07-17T22:18:27","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=604"},"modified":"2026-08-24T13:04:01","modified_gmt":"2026-08-24T13:04:01","slug":"pendulum-period-formula","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/pendulum-period-formula\/","title":{"rendered":"The Pendulum Period Formula"},"content":{"rendered":"\n
Definition<\/div>

\nPendulum period is the time a pendulum takes to complete one full swing \u2014 out and back again. For small swings it depends on only two things: T = 2\u03c0\u221a(L\/g), where L is the pendulum’s length and g is the local gravitational acceleration. On Earth, a 1.00 m pendulum has a period of about 2.0 seconds, whatever its mass.\n<\/p><\/div>\n

Legend has it that in 1583 a young Galileo Galilei sat in Pisa Cathedral, watching a lamp swing on its chain. Using his own pulse as a stopwatch, he noticed something odd: as the swings died down, each one still took the same time.<\/p>\n

Four centuries on, that observation runs grandfather clocks, metronomes, gravity surveys and a famous museum exhibit in Paris. The rule behind it is startlingly simple \u2014 the swing time is set by just two numbers, and neither of them is the mass.<\/p>\n

What Is the Pendulum Period?<\/h2>\n

The pendulum period is the time taken for one complete oscillation: the bob swings from its release point, across to the far side, and all the way back again. It is measured in seconds and given the symbol T.<\/p>\n

Watch out for a classic slip here. One swing across is only half a cycle \u2014 the period is the full round trip, out and back. Count “over-and-back” as one, or your measured period will be half the true value.<\/p>\n

Closely related is the frequency, f = 1\/T, the number of complete swings per second, measured in hertz. If you want the full story on that relationship, our guide to the frequency formula<\/a> covers it in depth. Physicists model all this with a “simple pendulum”: a small, heavy bob on a light string that doesn’t stretch.<\/p>\n

\"Pendulum<\/figure>\n

A simple pendulum: length L runs from the pivot to the centre of the bob, and gravity supplies a restoring force of mg sin \u03b8.<\/p>\n

The Pendulum Period Formula<\/h2>\n

The pendulum period formula is T = 2\u03c0\u221a(L\/g): the period equals two pi times the square root of the length divided by the gravitational acceleration. It holds for small swings, and it is one of the tidiest results in mechanics.<\/p>\n

T = 2\u03c0\u221a(L \/ g)<\/div>\n

Each symbol has a precise meaning:<\/p>\n