For small swings, a pendulum’s period depends only on its length and gravity, which made it the heart of accurate clocks for three centuries. A 0.994 m pendulum on Earth has a period of 2 s, a “seconds pendulum”.
How to use the Simple Pendulum Calculator
- Gravitational acceleration g
- Pendulum length L
- Every result field is editable: type into Period T or any other result and Pendulum length L plus every other field update to match.
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the length and gravity, or type a period into the result to find the length needed.
Inputs explained
| Field | What to enter |
|---|---|
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
| Pendulum length L | Units: m, cm, mm, km, in, ft … |
What each result means
- Period T = 2×pi×sqrt([Pendulum length L]÷[Gravitational acceleration g])
- Frequency f = 1÷[Period T]
- Angular frequency = 2×pi÷[Period T]
Example values
How the main result changes when Pendulum length L changes and everything else stays at the example values above:
| Pendulum length L (m) | Period T (s) |
|---|---|
| 0.5 | 1.4187 |
| 0.75 | 1.7376 |
| 1 | 2.0064 |
| 1.25 | 2.2432 |
| 1.5 | 2.4573 |
| 2 | 2.8375 |
Formula
T = 2π√(L/g), f = 1/T, L = g·T²/(4π²)
Worked example
Inputs: Gravitational acceleration g: 9.80665 m/s²; Pendulum length L: 1 m.
Results: Period T = 2.00641 s; Frequency f = 0.4984 Hz; Angular frequency = 3.13156 rad/s.
Key terms
- Period
- Time for one complete swing back and forth.
Frequently asked questions
Does the mass change the period?
No, only the length and g.
How long is a seconds pendulum?
About 0.994 m (period 2 s).
Is the formula exact?
It assumes small angles (below about 15°).
Would a pendulum clock run slower on the Moon?
Yes, about 2.46 times slower.