Vector Projection Calculator

Project vector a onto vector b (2D).

Scalar projection 3

Projection x 3

Projection y 0

Formula: projᵦa = (a·b / |b|²) · b

Step-by-step with your numbers:

1. Values used:

2. a x = 3

3. a y = 4

4. b x = 1

5. b y = 0

7. Scalar projection = 3

8. Projection x = 3

9. Projection y = 0

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The projection of a onto b is the shadow of a in the direction of b.

The math behind it

The scalar projection is (a·b)/|b|. The vector projection multiplies the unit vector of b by that amount: (a·b/|b|²)·b.

(3, 4) onto (1, 0) → scalar 3, vector (3, 0).

What if b is the zero vector?

Projection is undefined because you cannot divide by zero length.