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Math Calculators

Dot Product Calculator (2D)

Verified formula Updated Jun 2026 Private — runs on your device

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Verified formula Private

Dot product

10.0000

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Dot Product Calculator (2D)

The Dot Product Calculator (2D) works out your dot product in an instant. Enter vector a — x, vector a — y and vector b — x and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the vector a — x.
  2. Enter the vector a — y.
  3. Enter the vector b — x.
  4. Enter the vector b — y.
  5. Read off your dot product — the calculator updates automatically, with no button to press.

Formula

The Dot Product Calculator (2D) uses the formula:

Dot product = Vector A — x × Vector B — x + Vector A — y × Vector B — y

Worked example

For example, with vector a — x of 3, vector a — y of 4, vector b — x of 2 and vector b — y of 1, the dot product is 10.0000.

Inputs used
Vector A — x 3
Vector A — y 4
Vector B — x 2
Vector B — y 1
Results
Dot product 10.0000

Results are estimates for educational use, not professional advice.

Frequently asked questions

Multiply matching components and add them: a·b = ax·bx + ay·by. For (3,4) and (2,1) the dot product is 10.

It measures how much two vectors point in the same direction. Zero means they are perpendicular.

Yes. A negative dot product means the vectors point in generally opposite directions.

It is used to find angles between vectors, project one vector onto another, and compute work in physics.

The Dot Product Calculator (2D) uses the formula: Dot product = Vector A — x × Vector B — x + Vector A — y × Vector B — y. For example, with vector a — x of 3, vector a — y of 4, vector b — x of 2 and vector b — y of 1, the dot product is 10.0000.

Enter the vector a — x. Enter the vector a — y. Enter the vector b — x. Enter the vector b — y. Read off your dot product — the calculator updates automatically, with no button to press.

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