Calculates how long a simple pendulum takes to complete one full swing, based on its length.
How it works
The pendulum’s length is divided by standard gravity, then the square root of that ratio is multiplied by 2π to give the period.
What this does not include
This uses the small-angle approximation, accurate for swings under about 15-20 degrees — larger swing angles need a more complex formula this calculator doesn’t include.
How to use this calculator
- Enter the pendulum’s length.
A worked example
A pendulum 1 meter long: period = 2π√(L/g) = 2.0064 seconds per full swing.
A pendulum 2.5 meters long: period = 3.1724 seconds.
What the variables mean
| Variable | Meaning |
|---|---|
| Length | Length of the pendulum, from pivot to bob |
| g | Standard gravitational acceleration, 9.81 m/s² |
Edge cases worth knowing
Period depends on length and gravity only — not on mass or swing amplitude (for small swings). A heavier bob doesn’t swing faster or slower than a lighter one on the same length string.
A length of zero makes the period zero, which the calculator treats as an invalid input rather than a meaningful pendulum.
Frequently asked questions
Why doesn’t the pendulum’s mass affect its period?
For a simple pendulum (a point mass on a massless string), the period depends only on length and gravity — the mass cancels out of the equation entirely.
Why does a longer pendulum swing more slowly?
A longer pendulum has farther to travel on each swing, and the period grows with the square root of length, so it takes proportionally longer per swing.
Would this pendulum swing differently on the Moon?
Yes — with weaker gravity, the same-length pendulum would swing more slowly (a longer period) than on Earth.
