2D Vector Addition Calculator
Add two vectors and find the resultant magnitude and angle.
Enter your values
Enter the vector 1 x you are working with.
Enter the vector 1 y you are working with.
Enter the vector 2 x you are working with.
Enter the vector 2 y you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Add two vectors and find the resultant magnitude and angle. |
|---|---|
| Category | Math |
| Inputs needed | Vector 1 x, Vector 1 y, Vector 2 x, Vector 2 y |
| Main output | Resultant vector |
| Formula | R = (x1+x2, y1+y2), |R| = sqrt(Rx^2+Ry^2) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Vector 1 x
- Enter the vector 1 x you are working with.
- Vector 1 y
- Enter the vector 1 y you are working with.
- Vector 2 x
- Enter the vector 2 x you are working with.
- Vector 2 y
- Enter the vector 2 y you are working with.
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.
What do I need to enter into the 2D Vector Addition Calculator?
Just 4 values: vector 1 x, vector 1 y, vector 2 x, vector 2 y. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the 2D Vector Addition Calculator work out the answer?
Vectors add component-wise; the resultant's magnitude comes from the Pythagorean theorem and its angle from arctangent. It applies the formula R = (x1+x2, y1+y2), |R| = sqrt(Rx^2+Ry^2) and shows the working so you can check each step by hand.
Is the 2D Vector Addition Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.