Pendulum Period Calculator
Why a Longer Pendulum Swings Slower
A simple pendulum's swing time depends on almost nothing you'd expect — not its mass, not how far it swings (for small angles), just its length and the local strength of gravity. Galileo reportedly noticed this timing this consistency while watching a swinging chandelier, and the relationship became the basis for pendulum clocks that stayed accurate for centuries before quartz and atomic timekeeping took over.
The Formula
T is the period — the time for one full back-and-forth swing — L is the pendulum's length, and g is gravitational acceleration (9.81 m/s² metric, or 32.174 ft/s² imperial). This formula holds for small swing angles; larger amplitudes introduce a small correction this idealized version doesn't capture.
Why This Still Matters Today
- Mechanical clock design — pendulum clocks are tuned by adjusting length, since period depends on the square root of length rather than length directly.
- Seismometers — some early seismograph designs used pendulum principles to detect ground motion relative to a slow-swinging mass.
- Physics education — the pendulum is a standard way to introduce simple harmonic motion because its period is so easy to measure and predict.
- Amusement and playground equipment — swing timing and structural loads follow the same length-dependent period relationship.
Length Versus Period
Because period depends on the square root of length, doubling a pendulum's length doesn't double its period — it only increases it by about 41%:
| Length | Period |
|---|---|
| 0.25 m | 1.003 s |
| 0.994 m | 2.000 s (the classic "seconds pendulum") |
| 2.0 m | 2.837 s |
| 3.0 m | 3.475 s |
A pendulum roughly 0.994 m long takes almost exactly 2 seconds per swing — historically used to mark one second per half-swing in grandfather clocks.
How to Use This Calculator
- Enter the Pendulum Length.
- Choose Metric (meters, g = 9.81 m/s²) or Imperial (feet, g = 32.174 ft/s²).
- Select Calculate to get both the period in seconds and the corresponding frequency in Hz, along with the worked formula.
Related Calculations
For a different kind of periodic motion driven by a spring rather than gravity, see the Simple Harmonic Motion Calculator, or convert this period directly into frequency with the Frequency Calculator.