Enter the total value and the angle of the vector into the calculator to determine the vertical and horizontal components. This can be used to calculate the components of a velocity, force, or any other vector quantity.

Vertical & Horizontal Components Formula

The following formulas are used to calculate the horizontal and vertical components of a vector.

Vc = M * Sin (a)

Hc = M * Cos (a)

  • Where Vc is the vertical component
  • Hc is the horizontal component
  • M is the magnitude of the value/vector
  • a is the angle of the vector

What are the vertical & horizontal components?

Definition:

Vertical and horizontal components are the values of the base and height of a triangle formed with a vector as measured from the x-axis of a graph.

In other words, when the horizontal and vertical components are put together to form a triangle, the resulting hypotenuse is the original value/vector.

How to calculate vertical and horizontal components?

Example Problem:

The following example outlines how to calculate the vertical and horizontal components of a vector.

First, determine the magnitude of the vector. In this case, we are looking at a velocity, and the magnitude is measured to be 500 m/s.

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

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

Vc = M * Sin (a)

Hc = M * Cos (30)

Vc = 500 * Sin (30)

Hc = 500 * Cos (30)

Vc = 250 m/s

Hc = 433.012 m/s