Vector Projection Calculator
Project vector A onto vector B.
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ⓘ Live results
Results
- Scalar projection
- 3
- Vector projection
- (3, 0)
- Dot product A·B
- 3
Quick answer
The projection of A onto B is (A·B/|B|^2) times B, giving the component of A that lies along B's direction.
proj_B(A) = (A·B / |B|^2) * B
How to use the Vector Projection Calculator
- 1Enter the components of vectors A and B.
- 2The scalar projection is A·B divided by |B|.
- 3The vector projection scales B by A·B/|B|^2.
Worked example
Using the values the calculator loads with:
Inputs
- Vector A x3
- Vector A y4
- Vector B x1
- Vector B y0
Results
- Scalar projection3
- Vector projection(3, 0)
- Dot product A·B3
Frequently asked questions
What does projection mean intuitively?
It's the 'shadow' of A cast onto the line through B.
What if B is the zero vector?
Projection is undefined since you can't project onto a direction with zero length.
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.