Simple Pendulum Calculator

This simple pendulum calculator is a tool that will let you calculate the period and frequency of any pendulum in no time. Read on to learn the period of a pendulum equation and use it to solve all of your pendulum swing problems.

We made a video about pendulums! Watch it here:

First of all, a simple pendulum is defined to be a point mass or bob (taking up no space) that is suspended from a weightless string or rod. Such a pendulum moves in a harmonic motion — the oscillations repeat regularly, and kinetic energy is transformed into potential energy, and vice versa. (discover how it occurs with our simple harmonic motion calculator)

If you want to calculate the energy of the pendulum, make sure to use our kinetic energy calculator and potential energy calculator.

Surprisingly, for small amplitudes (small angular displacement from the equilibrium position), the pendulum period doesn't depend either on its mass or on the amplitude. It is usually assumed that "small angular displacement" means all angles between -15º and 15º. The formula for the pendulum period is:

T = 2π√(L/g)

where:

• T is the period of oscillations - the time that it takes for the pendulum to complete one full back-and-forth movement;
• L is the length of the pendulum (of the string from which the mass is suspended); and
• g is the acceleration of gravity. On Earth, this value is equal to 9.80665 m/s² — this is the default value in the simple pendulum calculator.

You can find the frequency of the pendulum as the reciprocal of the period:

f = 1/T = 1/[2π√(g/L)]

1. Determine the length of the pendulum. For example, it can be equal to 2 m.
2. Decide a value for the acceleration of gravity. We will use the Earthly figure of 9.80665 m/s², but feel free to check how the pendulum would behave on other planets.
3. Calculate the period of oscillations according to the formula above: T = 2π√(L/g) = 2π × √(2/9.80665) = 2.837 s.
4. Find the frequency as the reciprocal of the period: f = 1/T = 0.352 Hz.
5. You can also let this simple pendulum calculator perform all calculations for you!

For a pendulum with angular displacement higher than 15º, the period also depends on the moment of inertia of the suspended mass. This type of pendulum is studied in our physical pendulum calculator, and the equation for its period has the form of:

T = 2π√(I/mgD),

where:

• m is the mass of the pendulum;
• I is the moment of inertia of the mass; and
• D is the distance from the center of mass to the point of suspension.