Simple Pendulum Calculator
Calculate the period and frequency of a simple pendulum from its length and local gravity.
How it works
T = 2π·√(L / g) · frequency f = 1 / T
For small swings, a simple pendulum’s period depends only on its length and the local gravity — not on the mass of the bob or how far it swings. Longer pendulums swing more slowly, with the period growing as the square root of the length. This steady, predictable beat is what made pendulums the heart of accurate clocks for centuries.
Worked example
A 1 m pendulum on Earth (g = 9.81): T = 2π × √(1 ÷ 9.81) ≈ 2.006 s, giving a frequency of about 0.499 Hz — very close to a one-second half-swing.
Sources: Pendulum — Wikipedia
Frequently asked questions
Does the mass of the bob matter?
No. Like free fall, the period is independent of mass. A heavy and a light bob on strings of equal length swing at exactly the same rate.
Does the swing amplitude affect the period?
For small angles (under about 15°) the period is essentially constant — the property called isochronism. At large angles the period grows slightly and the simple formula becomes approximate.
How long is a one-second pendulum?
A pendulum with a period of 2 s (one second per swing) is about 0.994 m long on Earth. That is why grandfather clocks are roughly a metre in the pendulum.
Related calculators
Educational estimate. Check the formula and units for your exact case.