2D Vector Addition Calculator
Add two vectors and find the resultant magnitude and angle.
Enter your values
ⓘ Live results
Results
- Resultant vector
- (2, 6)
- Magnitude
- 6.3246
- Direction
- 71.57°
Quick answer
Vectors add component-wise; the resultant's magnitude comes from the Pythagorean theorem and its angle from arctangent.
R = (x1+x2, y1+y2), |R| = sqrt(Rx^2+Ry^2)
How to use the 2D Vector Addition Calculator
- 1Enter the x and y components of both vectors.
- 2Add them component-wise to get the resultant.
- 3Convert the resultant to magnitude-and-angle (polar) form.
Worked example
Using the values the calculator loads with:
Inputs
- Vector 1 x3
- Vector 1 y4
- Vector 2 x-1
- Vector 2 y2
Results
- Resultant vector(2, 6)
- Magnitude6.3246
- Direction71.57°
Frequently asked questions
Does order matter?
No, vector addition is commutative — A+B equals B+A.
How do I subtract vectors?
Enter the second vector's components as negative values.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.