Pendulum Period Calculator

T = 2π √(L/g). Period of a simple pendulum (small angles).

Inputs

Result

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General calculation reads

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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

Why no mass dependence?+
Restoring torque scales with mass; moment of inertia also scales with mass. Cancels.
Small-angle approximation?+
sin(θ) ≈ θ for small angles. Above ~10°, formula understates period by 1-2%; at 60° by ~7%.
Grandfather clock?+
Designed L ≈ 1 m → period 2 s. Tic-toc cadence comes from this.
Foucault pendulum?+
Demonstrates Earth's rotation: pendulum plane rotates over 24+ hours (depends on latitude).
Compound pendulum?+
Real (extended) pendulum: T = 2π √(I/mgd). Reduces to simple form for point mass.

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