Enter the mass and the angle between the pendulum and vertical into the calculator to determine the pendulum force.

Pendulum Force Formula

The following equation is used to calculate the Pendulum Force.

F = m*g*sin(a)

  • Where F is the pendulum force (N)
  • m is the mass of the pendulum (kg)
  • g is the acceleration due to gravity (m/s^2)
  • a is the angle of the pendulum relative to vertical (degrees)

What is a Pendulum Force?


Pendulum force is the gravitational force acting upon a pendulum as it swings. The pendulum’s mass is acted upon by gravity, and in turn, the pendulum transmits that force to the point where it meets its anchor, called the fulcrum. The force of gravity supplies the energy that causes a pendulum to move.

How to Calculate Pendulum Force?

Example Problem:

The following example outlines the steps and information needed to calculate the Pendulum Force.

First, determine the mass of the ball and string. In this example, the mass of the ball and string is 2 kg.

Next, determine the angle at which the pendulum is swinging. At the instant being analyzed, the pendulum is at a 45-degree angle.

Finally, calculate the pendulum force using the formula above:

F = m*g*sin(a)

F = 2*9.81*sin(45deg)

F = 13.873 N