How this calculator works
A simple pendulum treats the bob as a point mass on a massless inextensible string. At small angles, the restoring acceleration is proportional to angle, giving a nearly amplitude-independent period. Length runs from the pivot to the bob centre. The chart assumes release from rest and limits the release angle to 10 degrees; damping and large-amplitude corrections are omitted.
Formula
T = 2 pi sqrt(L/g); f = 1/T; L = g(T/(2 pi))²; theta(t) approximately theta_0 cos(2 pi t/T).
Worked example
If g = pi² m/s² and L = 1 m, the period is exactly 2 s and frequency 0.5 Hz. With the same gravity, a 4 s period requires a 4 m length.
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Frequently asked questions
Does bob mass change the period?
In this ideal model mass cancels. Real bobs can differ in drag and pivot behaviour.
Why limit the release angle?
The formula replaces sin(theta) by theta. Larger amplitudes increase the real period beyond this approximation.
Can I measure gravity with a pendulum?
Yes. Measure effective length and average the time of many small oscillations, then solve gravity from the period.