Pendulum Period Calculator
A simple pendulum's swing period depends only on its length and local gravity — not on how heavy the bob is or how wide the swing angle is (for small swings), which is a genuinely surprising and useful physical result.
Inputs
Result
2.0061 s
Frequency 0.4985 Hz
How it works
T = 2π√(L/g)
How the pendulum period calculator works
T = 2π√(L ÷ g), where L is the pendulum's length and g is local gravitational acceleration.
Worked example: 1 metre pendulum on Earth
- T = 2π × √(1 ÷ 9.81) = 6.2832 × 0.3193 ≈ 2.006 s.
- Frequency = 1 ÷ 2.006 ≈ 0.4985 Hz — just under one full swing per second.
Common mistakes to avoid
Assuming a heavier pendulum bob swings slower or faster
Mass doesn't appear anywhere in the formula — a heavier bob on the same length string has exactly the same period as a lighter one, for the same reason mass doesn't affect free-fall time.
Applying this formula to a wide swing angle
This exact formula is an approximation valid for small swing angles (typically under about 15-20°) — a pendulum swinging through a much wider arc takes measurably longer per swing than this formula predicts.
Frequently asked questions
Why doesn't the pendulum's mass affect its period?
Just as with free fall, a heavier bob experiences proportionally more gravitational force but also more inertia resisting acceleration — the two effects cancel, leaving period dependent only on length and gravity.
How is this used in real clock design?
Pendulum clocks rely on this length-gravity relationship for consistent timekeeping — historically, clockmakers would fine-tune the pendulum's effective length to correct a clock running fast or slow.
What happens to a pendulum's period on the Moon?
Lower gravity means a longer period for the same length — a pendulum clock accurate on Earth would run measurably slow if simply transported to the Moon without recalibration.
How does swing angle affect accuracy if it's not exactly small?
Larger swing angles introduce a period slightly longer than this small-angle formula predicts, growing more significant as the angle increases well beyond about 20°.
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