Pendulum Calculator
Find a simple pendulum's period from its length, or the length needed for a target period.
A simple pendulum swings with period T = 2π√(L/g), where L is the length and g is 9.81 m/s². The formula assumes small swings, so it holds best for angles under about 15°.
Length
1m
Period
2.0061s
Frequency
0.4985Hz
How it works
A simple pendulum is just a mass on a string, and its period — the time for one full back-and-forth swing — depends only on the length and gravity: T = 2π√(L/g). The mass on the end doesn't matter, and neither does how far you pull it back, as long as the swing stays small.
That length dependence is why a one-meter pendulum takes almost exactly two seconds per swing (about 2.006 s). Grandfather clocks lean on this: builders tune the rod length until each swing marks off a precise interval. Flip the calculation the other way and you can ask what length gives you any period you want.
The catch is the small-angle assumption. The neat formula holds when swings stay under roughly 15°; push the pendulum out to a wide arc and the real period stretches a little longer than the formula says. For classroom-sized swings, though, the difference is tiny.
Frequently asked questions
Does the weight on the end change the period?
No. A heavier bob doesn't swing any faster or slower — period depends only on length and gravity, not mass. That surprising fact is one of the classic results you can check with this calculator.
Why does length matter but amplitude doesn't?
For small swings, a wider pull gives the bob a longer path but also a proportionally higher speed, and the two effects cancel. Length changes the geometry of the whole swing, so it's the factor that actually sets the timing.
What gravity value does this use?
It uses 9.81 m/s², standard Earth gravity. On the Moon a pendulum would swing much more slowly, since weaker gravity means a longer period for the same length.