Math

Vector Addition Calculator

Add two 2D vectors and find the resultant magnitude and direction.

Calculated Output

Resultant x 4

Resultant y 2

Magnitude 4.472

Direction (°) 26.565

Formula: a + b = (aₓ + bₓ, a_y + b_y)

Step-by-Step Breakdown

1. Values used:

2. a x = 3

3. a y = 4

4. b x = 1

5. b y = -2

7. Resultant x = 4

8. Resultant y = 2

9. Magnitude = 4.472

10. Direction = 26.565°

Did this calculator solve your problem today?

The math behind it

Add x-components and y-components separately. The magnitude is √(rₓ² + r_y²) and the direction is atan2(r_y, rₓ).

(3, 4) + (1, −2) = (4, 2), magnitude ≈ 4.47.

Can I subtract vectors the same way?

Yes — subtract the components instead of adding them.