Vector Projection Calculator
Project vector A onto vector B.
Enter your values
Enter the vector a x you are working with.
Enter the vector a y you are working with.
Enter the vector b x you are working with.
Enter the vector b 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.
- 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
At a glance
| What it does | Project vector A onto vector B. |
|---|---|
| Category | Math |
| Inputs needed | Vector A x, Vector A y, Vector B x, Vector B y |
| Main output | Scalar projection |
| Formula | proj_B(A) = (A·B / |B|^2) * B |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Vector A x
- Enter the vector a x you are working with.
- Vector A y
- Enter the vector a y you are working with.
- Vector B x
- Enter the vector b x you are working with.
- Vector B y
- Enter the vector b y you are working with.
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.
What do I need to enter into the Vector Projection Calculator?
Just 4 values: vector a x, vector a y, vector b x, vector b 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 Vector Projection Calculator work out the 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. It applies the formula proj_B(A) = (A·B / |B|^2) * B and shows the working so you can check each step by hand.
Is the Vector Projection 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.