Enter the x and y components of a force vector into the calculator to determine the magnitude of the force.

Magnitude of Force Formula

The following equation is used to calculate the magnitude of a force.

Fm = √(Fx^2 + Fy^2)
  • Where Fm is the magnitude of the force
  • Fx is the x-component of the force vector
  • Fy is the y-component of the force vector

To calculate the magnitude of a force, add together the x-component squared by the y-component squared, then take the square root of that value.

What is a Magnitude of Force?


In physics, a force is the push or pull that acts upon an object to make it move or accelerate. A force is said to have a magnitude (or strength) and direction.

The force can be expressed as a vector like a velocity, position, and acceleration. This vector has an x and y-component, which both contribute to the overall magnitude of the force.

How to Calculate Magnitude of Force?

Example Problem:

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

First, determine the x-component of the force. In this example, the x-component of force is given as 50N.

Next, determine the y-components of force. In this case, the y-component of force is given as 30N.

Finally, calculate the magnitude of force using the formula above:

Fm = SQRT(Fx^2 + Fy^2)

Fm = SQRT(50^2 + F30^2)

Fm = 58.309 N