Enter the total value and the vector’s angle 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

To calculate the vertical component, multiply the magnitude by the sine of the angle. To calculate the horizontal component, multiply the magnitude by the cosine of the angle.

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

FAQ

What is the significance of calculating the vertical and horizontal components of a vector?

Calculating the vertical and horizontal components of a vector is crucial in physics and engineering because it allows for the analysis of forces, velocities, and other vector quantities in two dimensions. This simplifies problems, making it easier to apply principles such as Newton’s laws of motion.

Can these formulas be applied to any vector quantity?

Yes, the formulas for calculating the vertical (Vc = M * Sin (a)) and horizontal (Hc = M * Cos (a)) components can be applied to any vector quantity, including force, velocity, displacement, and acceleration, as long as you know the magnitude and the angle of the vector.

How do you determine the angle of a vector?

The angle of a vector is typically measured from the positive x-axis in a counter-clockwise direction in a Cartesian coordinate system. It can be determined using trigonometric relationships in a right-angled triangle formed by the vector or through measurement using tools such as a protractor in physical scenarios.