Pendulum Length Calculator
Find the length a simple pendulum needs for a chosen swing period — including the classic one-second (seconds) pendulum.
How it works
L = g · (T / 2π)² (rearranged from T = 2π·√(L/g))
A simple pendulum’s period depends only on its length and gravity, not on the mass of the bob or (for small swings) the size of the swing. Rearranging the period formula lets you design a pendulum backwards: pick the swing time you want and solve for the length. The classic "seconds pendulum", which takes one second per half-swing (a two-second full period), works out to just under a metre.
Worked example
For a 2 s period on Earth (g = 9.81): L = 9.81 × (2 ÷ 2π)² = 9.81 × 0.3183² ≈ 0.994 m — the famous seconds pendulum, close to one metre.
Sources: Pendulum — Wikipedia
Frequently asked questions
What counts as one period here?
One full period is a complete back-and-forth swing — from one side, through the bottom, to the other side and all the way back. A grandfather clock’s "tick" and "tock" together make one period.
Does the bob’s weight change the length needed?
No. The period of a simple pendulum is independent of mass, so a heavier bob needs exactly the same length. Only the swing time and local gravity set the length.
Why does this assume a small swing?
The neat formula holds for small angles (under about 15°). For wide swings the real period is slightly longer, so a pendulum built to this length would run marginally slow at large amplitude.
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Educational estimate. Check the formula and units for your exact case.