Vector Scalar Product Calculator
Calculate the dot (scalar) product, magnitudes, angle, and projection for two matching 2D or 3D vectors.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 20, 2026 · Editorial method
Calculate dot product and angle
Dot product formula
A · B = a₁b₁ + a₂b₂ + a₃b₃ = |A||B|cos θ
The result is a scalar. A positive product indicates an acute angle, zero indicates orthogonality for nonzero vectors, and a negative product indicates an obtuse angle.
Projection included
The vector projection of A onto B is (A·B / |B|²)B. A zero vector has no direction, so its angle and use as the projection axis are undefined. See OpenStax's explanation of the dot product.