Pendulum Period Calculator
A pendulum’s period from its length — and the surprising fact that mass does not appear in the answer.
For small swings the period is 2π√(L/g).
How the pendulum period calculator works
For small swings the period is 2π√(L/g). Mass is absent, which is the fact that makes pendulums useful as clocks: a heavier bob does not swing slower.
Amplitude is absent too, but only approximately. The small-angle approximation drifts about 0.2% at 10 degrees and 1.7% at 30, which is exactly why pendulum clocks are built with tiny swings.
Formula: T = 2π√(L/g)
Worked examples
| Inputs | Period (s) | Note |
|---|---|---|
| A one-metre pendulum | 2.00641 | 2.006 s |
| A wide swing | 2.00641 | 4% slower than the formula says |
| A seconds pendulum | 2.00038 | two seconds — the grandfather clock |
FAQFrequently asked questions
Does mass affect a pendulum?
No. The period depends only on length and gravity, which is why a pendulum makes a good clock and a bad scale.
Why is the small-angle approximation used?
Because the exact solution needs an elliptic integral. Below about 10 degrees the approximation is within 0.2%, which is close enough for almost everything.
How long is a seconds pendulum?
About 0.994 m for a two-second period — one second each way. It is why grandfather clocks are the height they are.
What happens on the Moon?
The period lengthens by a factor of √(9.81/1.62), about 2.46 times. A pendulum clock taken to the Moon runs badly slow.
Does amplitude really not matter?
Approximately, and that near-independence is called isochronism. It was Galileo's observation and it is only true for small swings.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.