Enter the mass and angle of the gyration into the calculator to determine the gyroscopic force.

Gyroscopic Force Formula

The following equation is used to calculate the Gyroscopic Force.

Fg = m*g*sin(a)

  • Where Fg is the gyroscopic force (N)
  • m is the mass of the gyroscope (kg)
  • g is the acceleration due to gravity (9.81 m/s^2)
  • a is the angle of the gyration from vertical (degrees)

What is a Gyroscopic Force?


Gyroscopic force, also known as gyroscopic inertia, is an inertial force explained by the law of conservation of angular momentum. This law states that the angular momentum remains constant unless acted upon by an external torque.

A gyroscope is a device consisting of a rapidly spinning wheel mounted on a base that allows it to tilt freely in any direction. The gyroscopic force plays a significant role in the operation of the gyroscope.

How to Calculate Gyroscopic Force?

Example Problem:

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

First, determine the mass of the gyroscope. In this example, the mass is determined to be 12.5 kg.

Next, determine the angle of the gyration relative to vertical. In this case, the angle is found to be 25 degrees.

Finally, calculate the gyroscopic force using the formula above:

Fg = m*g*sin(a)

Fg = 12.5*9.81*sin(25deg)

Fg = 51.82 N