Vertical & Horizontal Component Calculator

To find the vertical and horizontal components of a vector, multiply the magnitude of the vector by the sine or cosine of the angle, respectively.

The Vertical & Horizontal Component Calculator is a tool designed to determine the individual components of a vector. This is useful in physics, engineering, and mathematics to break down forces, velocities, or displacements into their perpendicular components for easier analysis.

Inputting the magnitude and the angle, you can quickly calculate the vertical and horizontal components for any given vector.

Formula:

Contents

1 Formula:
2 Solved Calculations:
3 What is the Vertical & Horizontal Component Calculator?
4 Final Words:

Vertical Component: $V_c = M \cdot \sin(a)$
Horizontal Component: $H_c = M \cdot \cos(a)$

Variable	Description	Unit
$V_c$	Vertical component of the vector	Same as $M$
$H_c$	Horizontal component of the vector	Same as $M$
$M$	Magnitude of the vector	Any measurable unit
$a$	Angle of the vector (with horizontal)	Degrees or radians

Solved Calculations:

Example 1: Find Components for $M = 10$ , $a = 30^\circ$

Step	Value	Explanation
Magnitude ( $M$ )	$10$	Given
Angle ( $a$ )	$30^\circ$	Given
Vertical Component ( $V_c$ )	$10 \cdot \sin(30^\circ) = 10 \cdot 0.5$	Multiply magnitude by sine
Horizontal Component ( $H_c$ )	$10 \cdot \cos(30^\circ) = 10 \cdot 0.866$	Multiply magnitude by cosine
Result	$V_c = 5, H_c = 8.66$	Vertical and horizontal components

Example 2: Find Components for $M = 20$ , $a = 45^\circ$

Step	Value	Explanation
Magnitude ( $M$ )	$20$	Given
Angle ( $a$ )	$45^\circ$	Given
Vertical Component ( $V_c$ )	$20 \cdot \sin(45^\circ) = 20 \cdot 0.707$	Multiply magnitude by sine
Horizontal Component ( $H_c$ )	$20 \cdot \cos(45^\circ) = 20 \cdot 0.707$	Multiply magnitude by cosine
Result	$V_c = 14.14, H_c = 14.14$	Vertical and horizontal components

What is the Vertical & Horizontal Component Calculator?

The Vertical & Horizontal Component Calculator is a useful tool for breaking down vectors, forces, or velocities into their vertical and horizontal components.

Final Words:

To conclude, the Vertical & Horizontal Component Calculator is an essential resource for resolving vectors efficiently. It simplifies calculations, aids in problem-solving, and provides clarity in understanding motion and force components.