Vector Addition Calculator
Add two or more vectors together and get the resultant magnitude and direction in 2D or 3D, free and instant in your browser.
Enter Values
How to use this calculator
- Enter the x and y components of both vectors.
- Read the resultant, magnitude and direction.
How it works
Add the components: resultant = (ax+bx, ay+by). Magnitude = √(x²+y²); direction = atan2(y, x).
Worked example
(3,4) + (1,2). = (4,6), magnitude 7.21, 56.31°.
Common mistakes
- Adding magnitudes directly — you must add the components, not the lengths.
- Mixing up the angle reference (this is measured from the +x axis).
Frequently asked questions
How do I add two vectors?
Add their components: (a1, a2) + (b1, b2) = (a1 + b1, a2 + b2). The tool also gives the resultant's magnitude and direction.
What is the resultant of two vectors?
The single vector with the same effect as both combined — found tip-to-tail or by adding components.
What direction is 0°?
Along the positive x-axis, increasing anticlockwise — standard mathematical convention.
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Cite this tool
Zerdly. (2026). Vector Addition Calculator. Retrieved from https://www.zerdly.com/tools/vector-addition-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.