Pendulum Period Calculator
T = 2π √(L/g). Period of a simple pendulum (small angles).
Result
Period
2.0061 s
Frequency: 0.4985 Hz.
- Length1 m
- Gravity9.81 m/s²
- Period2.006067 s
- Frequency0.498488 Hz
- Half period (one swing)1.003033 s
Step-by-step
- T = 2π √(L/g) = 2π × √(1 / 9.81) = 2.006067 s.
- f = 1/T = 0.498488 Hz.
How to use this calculator
- Enter pendulum length and local g.
- Read period + frequency.
About this calculator
A simple pendulum (point mass on massless string) has period T = 2π √(L/g) for small swings (≤ ~10°). Period independent of mass and (initially) amplitude — the discovery that made grandfather clocks possible. A 1m pendulum on Earth: T ≈ 2.0 s. To halve the period, shorten by 4×. To increase period 10×, lengthen 100×. Foucault pendulum demonstrates Earth's rotation.
Frequently asked
Restoring torque scales with mass; moment of inertia also scales with mass. Cancels.
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