Rule of thumb · PhysicsNº 86 / 167

Pendulum period: √length, not mass

Quadruple a pendulum’s length and it swings half as fast. Mass doesn’t matter at all.

Why it works

T ∝ √L, and mass cancels out of the equation entirely — same reason heavy and light objects fall together.

When it fails

Mass stops being irrelevant the moment the pendulum is not a simple one. A physical pendulum's period depends on where the mass sits, through its moment of inertia — which is why a metronome changes tempo when you slide the weight without changing its mass at all.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Pendulum Simulator →

More in Physics

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Does a heavier pendulum swing slower?

Quadruple a pendulum’s length and it swings half as fast. Mass doesn’t matter at all. T ∝ √L, and mass cancels out of the equation entirely — same reason heavy and light objects fall together.

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