Pendulum Period Calculator
Calculate the swing period of a simple pendulum from its length.
Assumptions used in this calculation
- Small-angle, ideal pendulum: Assumes a small swing angle, a massless rigid rod/string, and no air resistance or friction at the pivot.
About this calculator
Grandfather clocks, playground swings, and physics lab experiments all rely on a strikingly simple fact: a pendulum's swing period depends only on its length and local gravity, not its weight or how far it swings, but confirming that with the actual formula still requires handling a square root and π correctly. This calculator computes the period of a simple pendulum, the time for one complete back-and-forth swing, using the small-angle approximation T = 2π√(L/g), where L is the pendulum's length and g is Earth's standard gravitational acceleration (9.80665 m/s²). Enter just the length and it returns the period directly. Because the mass term cancels out of the underlying equations of motion entirely, a heavy bob and a light one of the same length swing at exactly the same rate, a genuinely counterintuitive result confirmed by this formula. The small-angle approximation holds within about 1% error for swings under 15-20°, wider swings take measurably longer than this calculator predicts.
Worked example
1m pendulum
Result: 2.006 s
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