Dot Product Calculator

Positive result: Vectors point in similar directions
Zero result: Vectors are perpendicular (orthogonal)
Negative result: Vectors point in opposite directions

Calculate the dot product of two vectors with step-by-step breakdown.

Number of Dimensions

Vector A

Vector B

About the Dot Product

The dot product (also called scalar product or inner product) is a fundamental vector operation that returns a scalar value.

A · B = Σ(aᵢ × bᵢ) = a₁b₁ + a₂b₂ + ... + aₙbₙ