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Simple Pendulum Period Calculator

Solve for a pendulum's period, length, or the local gravitational acceleration using the small-angle simple pendulum formula.

Period
2.0061 s
Length
1 m
Gravitational acceleration
9.81 m/s²

How it works

For small swing angles, a simple pendulum's period is T = 2π√(L/g), where L is the length from the pivot to the bob's center of mass and g is the local gravitational acceleration. Pick which quantity to solve for; the calculator rearranges the same formula to find it from the other two — L = g(T/2π)² when solving for length, or g = L(2π/T)² when solving for gravity.

Length and gravitational acceleration only need to share the same length unit (both in meters, or both in feet) for the formula to work — L/g always comes out in units of time² regardless of which length unit is used, so the period is in seconds either way, the same unit-agnostic reasoning this site's projectile motion calculator uses for its own velocity/gravity pair.

This is the small-angle approximation, accurate for swing amplitudes up to roughly 15-20° from vertical; a real pendulum swung much wider than that takes slightly longer per swing than this formula predicts.

FAQ

Why does gravitational acceleration default to 9.81?

9.81 m/s² is Earth's standard average gravitational acceleration at sea level. It's a normal, editable field rather than a hardcoded constant, so the same formula works for a pendulum on the Moon (about 1.62 m/s²) or anywhere else if you change it.

Can I use this to measure the local value of g?

Yes — this is essentially the classic physics-lab method: time a pendulum of known length over several swings to get an accurate period, then solve for gravity. The longer the pendulum and the more swings you average, the less a timing error affects the result.

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