Vector Addition Calculator
Combining Two Directions Into One
Adding vectors combines two separate magnitudes-and-directions — two velocities, two forces, two displacements — into the single net effect they produce together. Unlike ordinary number addition, the result depends on direction as much as size, but the arithmetic itself stays simple: add each matching component separately.
The Formula
2D: A + B = (Ax+Bx, Ay+By)
3D: A + B = (Ax+Bx, Ay+By, Az+Bz)
3D: A + B = (Ax+Bx, Ay+By, Az+Bz)
Worked Example
Adding vector A = (3, 4) and vector B = (1, 2):
| Component | Calculation | Result |
|---|---|---|
| x | 3 + 1 | 4 |
| y | 4 + 2 | 6 |
Resulting vector: (4, 6).
Where This Matters
- Force analysis — combining multiple forces acting on an object to find the net force, a core step in statics and structural engineering.
- Navigation — adding a vehicle's velocity vector to a wind or current vector to find actual ground-track speed and direction.
- Game physics — summing movement, gravity, and impulse vectors each frame to update an object's position.
How to Use This Calculator
- Choose the dimension: 2D Vectors or 3D Vectors.
- Enter Vector A's x, y (and z for 3D) components.
- Enter Vector B's x, y (and z for 3D) components.
- Select Calculate to get the resultant vector.
Related Calculations
Need the length of the result? Use the Vector Magnitude Calculator, or find the angle between two vectors with the Angle Between Vectors Calculator.