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Vector Addition Calculator

Physics
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Calculates the sum of two or more vectors. Enter the x and y components of each vector, and the calculator will determine the resultant vector.

How To Use

How to use this calculator

Start with your values, or try a preset.

Step 1

Enter Vector 1 X component, Vector 1 Y component, Vector 2 X component, Vector 2 Y component, Vector 3 X component (optional), and Vector 3 Y component (optional) in the units shown.

Step 2

Read Resultant Y component, Resultant X component, Resultant Angle (degrees), and Resultant Magnitude in the results panel. Results update as you change the inputs.

Step 3

Choose a preset to load an example, then adjust the values for your situation.

Worked Examples

Example calculations

See the inputs and their calculated results.

Example 1: (3,4) + (5,12)

Vector 1 X component: 3 units; Vector 1 Y component: 4 units; Vector 2 X component: 5 units; Vector 2 Y component: 12 units; Vector 3 X component (optional): 0 units; Vector 3 Y component (optional): 0 units

Resultant Y component: 16 units; Resultant X component: 8 units; Resultant Angle (degrees): 63.43 degrees; Resultant Magnitude: 17.88854382 units

Example 2: (1,0) + (0,1)

Vector 1 X component: 1 units; Vector 1 Y component: 0 units; Vector 2 X component: 0 units; Vector 2 Y component: 1 units; Vector 3 X component (optional): 0 units; Vector 3 Y component (optional): 0 units

Resultant Y component: 1 units; Resultant X component: 1 units; Resultant Angle (degrees): 45 degrees; Resultant Magnitude: 1.414213562 units

Example 3: (2,2) + (-1,3)

Vector 1 X component: 2 units; Vector 1 Y component: 2 units; Vector 2 X component: -1 units; Vector 2 Y component: 3 units; Vector 3 X component (optional): 0 units; Vector 3 Y component (optional): 0 units

Resultant Y component: 5 units; Resultant X component: 1 units; Resultant Angle (degrees): 78.69 degrees; Resultant Magnitude: 5.099019514 units

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