Vector Addition Calculator

Vector Addition Calculator calculator can be used to add two vectors in Cartesian coordinates and display the result in component form and magnitude-angle form.

Input Parameters

Vector 1

Vector 2

Calculation Results

Calculation Formula

Result = Vector 1 + Vector 2

Where:
Result = (Vx1 + Vx2) i + (Vy1 + Vy2) j

Result in Component Form:

Result in Magnitude-Angle Form:

Vector Addition Calculator Calculator Usage Guide

Learn how to use the Vector Addition Calculator calculator and its working principles

How to Use the Calculator

  1. Enter the X and Y components of the first vector in the "Vector 1" section.
  2. Enter the X and Y components of the second vector in the "Vector 2" section.
  3. Click the "Calculate" button to compute the result.
  4. The result will be displayed in both component form (X and Y components) and magnitude-angle form (magnitude and angle in degrees).

Understanding Vector Addition

Vector addition is the operation of adding two or more vectors together to obtain their sum or resultant. In Cartesian coordinates, the addition of two vectors is performed by adding their corresponding components.

Formula

If Vector 1 = (Vx1, Vy1) and Vector 2 = (Vx2, Vy2), then their sum (Result) is:

Result = (Vx1 + Vx2) i + (Vy1 + Vy2) j

Result Interpretation

Component Form: The result is expressed as (Rx, Ry), where Rx is the X component and Ry is the Y component of the resultant vector.

Magnitude: The magnitude of the resultant vector is calculated using the Pythagorean theorem: √(Rx² + Ry²).

Angle: The angle of the resultant vector with respect to the positive X-axis is calculated using the arctangent function: atan2(Ry, Rx).