Pendulum period T–
Ticks per minute–
Escape wheel turns once every–
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The pendulum formula

For small swings, a pendulum's full back and forth period is T = 2 pi x sqrt(L / g), where L is the length to the center of mass and g is 9.81 m/s². Mass does not appear: a heavy bob and a light bob of the same length keep the same time.

A length of about 0.99 m gives a two second period, one tick each way. That is the classic seconds pendulum found in tall case clocks.

Try it: set the length to 0.99 m and the escape wheel to 30 teeth. The wheel turns once in about 60 seconds, so a seconds hand can sit right on its arbor. Now try 0.25 m and see the wheel race around in about 30 seconds.

Why the escapement matters

The anchor escapement, introduced in the 1600s, needs only a small swing. Small swings keep the period very close to the ideal formula, which made pendulum clocks accurate to seconds per day. In this teaching model the escape wheel moves half a tooth at each beat; real pallets also slide and give the pendulum a small impulse.

Sources

How to cite this model

Avid Solutions International. (2026, November 11). How a pendulum clock keeps time [Interactive 3D model]. Avid Field Lab. https://avidsolutionsintl.com/explore/clock-escapement

Last updated November 11, 2026

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