For small swings, a pendulum’s period depends only on its length and gravity, not its mass, which made pendulum clocks possible.
How to use the Simple Pendulum Calculator
- Length
- Gravitational acceleration
- Want to work backwards? Type a value into Period and Length is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Divide length by gravitational acceleration, take the square root and multiply by 2π.
Inputs explained
| Field | What to enter |
|---|---|
| Length | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration | Units: m/s², ft/s², g |
What each result means
- Period = 2×pi×sqrt([Length]÷[Gravitational acceleration])
- Frequency = 1÷[Period]
Example values
How the main result changes when Length changes and everything else stays at the example values above:
| Length (m) | Period (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)Worked example
Inputs — Length: 1 m; Gravitational acceleration: 9.80665 m/s².
Results — Period = 2.0064 s; Frequency = 0.4984 Hz.
Frequently asked questions
How long is a seconds pendulum?
About 0.994 m, giving a 2-second period.
Is the formula exact?
It assumes small angles, under about 15°.
What formula does the Simple Pendulum Calculator use?
T = 2π √(L ÷ g).
Can I work backwards from the result?
Yes. Type the result you want into Period and the calculator finds the matching length.