Math

Dot Product Calculator

Scalar product and angle between vectors.

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Results
Dot product
-15
Angle between
122.073°
|a|
6.16441
|b|
4.58258
Perpendicular?
No

Quick answer

The dot product multiplies matching components and sums them, giving |a||b|cos θ.

a · b = Σ aᵢbᵢ = |a||b|cos θ

How to use the Dot Product Calculator

  1. 1Enter the components of vector a.
  2. 2Enter the components of vector b.
  3. 3Both vectors must have the same length.

Frequently asked questions

What does a zero dot product mean?

The vectors are perpendicular.

Is the result a vector?

No, the dot product is a single number (a scalar).