Dot product calculator calculates the dot product of two vectors a and b in Euclidean space. Enter i, j, and k for both vectors to get scalar number.

a . b

Vector dot product calculator shows step by step scalar multiplication.

What is dot product?

Dot product is an algebraic operation that takes two equal-length sequences of numbers usually coordinate vectors, and returns a single number.

Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.

a . b usually read as a dot b.

Dot product

Image credit: “Dot Product” by Math is Fun.

Dot product formula

Use this equation to calculate dot product of two vectors.

a × b = |a| |b| cos(θ)


|a| is length of vector a

|b| is length of vector b

θ is the angle between a and b

We can also find dot product by using the points of both vectors.

(ai aj ak) . (bi bj bk) = (ai . bi + aj . bj + ak . bk)


 i, j, and k refers to x, y, and z coordinates on Cartesian plane.



Dot Product Formula from