Created By : Vaibhavi Kumari

Reviewed By : Phani Ponnapalli

Last Updated : May 17, 2023

You can find the time period or length of the pendulum in a blink of an eye using our free Simple Pendulum Calculator. To make your calculations easier and faster, simply enter the acceleration due to gravity and pendulum length in the below input fields and press the calculate button.

Choose a Calculation
Acceleration due to gravity(g):
Pendulum Length(L):

What is a Simple Pendulum?

The mass suspended from a rod is referred to as a simple pendulum. The pendulum means the position is defined as a straight vertical line passing through the fixed position.

The following are the most essential factors of the simple pendulum

  • The length of the pendulum is the distance between the centre of mass and the point of suspension, and it is represented by L.
  • The oscillatory motion of a simple pendulum is periodic to and fro motion of the pendulum, and the equilibrium is the mid-point of the oscillation.
  • The time it takes the pendulum to complete one full oscillation is known as the time period of the simple pendulum, and it is represented by the letter T.
  • The distance travelled by a simple pendulum from one side to the equilibrium position is its amplitude.

Period of Simple Pendulum Formula

The following are the formulas for calculating the simple pendulum period and frequency T = 2π × √(L/g), f = 1/T

  • Where, T = time period of the pendulum
  • f = frequency of the pendulum
  • L = length of the pendulum
  • g = acceleration due to gravity


How do you calculate the period of a simple pendulum?

Here are the easy guidelines for calculating the simple pendulum time period and frequency.

  • Step 1: Calculate the gravitational acceleration and the length of the pendulum.
  • Step 2: Divide the length by gravity's acceleration and take the square root of the result.
  • Step 3: The time period is calculated by multiplying the value obtained in the previous step by 2π.
  • Step 4: The frequency of the pendulum is the reciprocal of the time period.

For more concepts check out physicscalculatorpro.comto get quick answers by using this free tool.

How to Use the Simple Pendulum Calculator?

The following is the procedure how to use the simple pendulum calculator

  • Step 1: In the appropriate input fields, enter the length (L), gravity acceleration (g), and x for the unknown.
  • Step 2: To calculate the time period, click the "Calculate the Unknown" button.
  • Step 3: Finally, the output field will show the value of x.

Simple Pendulum Examples

Question 1:Find the time period and frequency of a simple pendulum with a length of 30 metres.


Given: L = 30 m

g = 9.8 m/s

Time Period T = 2π × √(L/g)

T = 2π × √(30/9.8)

= 2π × √(30/9.8)

= 2π × √(3.0612)

= 10.99

frequency f = 1/T

f = 1/10.99

= 0.09

As a result, the simple pendulum's average period and frequency are 10.99 seconds and 0.09 oscillations per second, respectively.

FAQs on Simple Pendulum Calculator

1. What are the three simple pendulum laws?

The three laws of a pendulum are as follows

  • A pendulum's time of oscillation is independent of its amplitude when its length is constant.
  • The shape, size, and material of a simple pendulum of constant length have no bearing on the period of oscillation.
  • A pendulum's time period is related to the square root of the length of a simple pendulum.


2. What is the formula for calculating the pendulum's length?

L = (T²g)/(4π²) is the formula for calculating the length of a simple pendulum.

3. What is the pendulum's oscillation?

Oscillation refers to a pendulum that swings from one extreme to the other before returning to its original point.

4. How do you calculate a pendulum's kinetic energy?

The kinetic energy would be KE= 1/2mv^2, where m is the pendulum's mass and v is the pendulum's speed. The pendulum is briefly immobile at its highest point.

5. What are the uses of a simple pendulum?

The clock, wrecking ball, ballistic pendulum, bowling ball, Foucault's pendulum, and metronome are all real-time uses of a simple pendulum.