Vector Dot Product
Free Vector Dot Product calculator with clear step-by-step results.
About Vector Dot Product
The dot product measures how aligned two vectors are.
Formula
Formula
A·B = ax·bx + ay·by
Worked example
With the default values below, Vector Dot Product returns Dot Product of 11.000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Vector A x
- 1
- Vector A y
- 2
- Vector B x
- 3
- Vector B y
- 4
Results
- Dot Product
- 11.000
- |A|
- 2.236
- cos θ
- 0.9839
Step by step
- 1Values used
- 2Formula
- 3Dot Product= 11.000
- 4|A|= 2.236
- 5cos θ= 0.9839
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does this calculator work?
The dot product measures how aligned two vectors are.
Why does this matter?
Zero means the vectors are perpendicular.