Pendulum Period Calculator

Find the period and frequency of a simple pendulum.

Inputs

m
Formulas
T = 2π·√(L / g)
f = 1 / T

Results

Period s
Frequency Hz

The simple pendulum

A simple pendulum is a mass swinging on a light string. For small swing angles its motion is simple harmonic, and its period depends only on the string length and the local gravity: T = 2π√(L/g). Remarkably, the period is independent of the mass and of the amplitude (for small angles).

T = 2π·√(L / g)

Period and frequency

The period T is the time for one complete swing, and the frequency f = 1/T is the number of swings per second. Longer pendulums swing more slowly. This relationship is why pendulum clocks keep accurate time and why pendulums can be used to measure g.

Frequently asked questions

Does mass change the period?

No. For a simple pendulum the period depends only on length and gravity, not on the mass of the bob.

Why must the angle be small?

The simple formula assumes the restoring force is proportional to displacement, which is only accurate for small angles, roughly under 15 degrees.

Read the full guide