Enter the magnitude of the force and the direction angle into the calculator to determine the horizontal and vertical forces.

Horizontal/Vertical Force Formula

The following equation is used to calculate the Horizontal/Vertical Force.

Fx = F * cos(a)

Fy = F * sin(a)

• Where F is the magnitude of the force
• a is the angle (degrees)
• Fx is the horizontal force
• Fy is the vertical force

What is a Horizontal and Vertical Force?

Definition:

A horizontal force is a force that is applied parallel to the ground, such as pushing or pulling a box across the floor. A vertical force is a force that is applied perpendicular to the ground, such as holding a weight over your head.

More specifically, a horizontal force is the x-component of a force vector, and a vertical force is the y-component of a force vector.

How to Calculate Horizontal/Vertical Force?

Example Problem:

The following example outlines the steps and information needed to calculate the horizontal and vertical forces of a force vector.

First, determine the magnitude of the force. In this example, the magnitude of the force is calculated to be 275 N.

Next, determine the direction of the force. For this problem, the angle of the vector is measured to be 30 degrees.

Finally, calculate the horizontal and vertical components of the force using the formula above:

Fx = F * cos(a)

Fy = F * sin(a)

Fx = 275* cos(30) = 238.15 N

Fy = 275* sin(30) = 137.5 N