Simple Pendulum Calculator

Your details

Choose which quantity to calculate. Supply the other three values.
Distance from the pivot point to the centre of the bob.
m
Pick a planet or enter your own value below.
Period (T)Earth-like gravity
2.0064s

Time for one complete oscillation

Frequency (f)0.4984Hz
Length (L)1
Gravity (g)9.8067m/s^2
Angular frequency (omega)3.1316rad/s
Formula validityValid for swing angles up to about 15 degrees (small-angle approximation).
2.0064 s
Very short<0.5Short0.5-1.5Typical1.5-2.5Long2.5-5Very long5+

Period: 2.0064 s - Frequency: 0.4984 Hz

  • The pendulum completes one full oscillation every 2.006 s, giving a frequency of 0.4984 Hz.
  • At a length of 1.000 m and g = 9.807 m/s^2, the small-angle formula T = 2pi * sqrt(L/g) gives this result.
  • A classic "seconds pendulum" (T = 2 s) on Earth requires a length of about 0.994 m.
  • The small-angle formula is accurate to within 1% for amplitudes up to about 15 degrees. Larger swings require elliptic integral corrections.

Next stepTo find the length needed for a given period, switch "Solve for" to Length and enter your desired period.

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