Mathematical Calculators

Dot Product Calculator

Calculate mathematical dot products, scalar products and dot product angles easily for your vectors.

Vector A

Vector B

Results

Table of contents

About scalar product calculator
How to use dot product calculator?
What is a dot product?
What is the formula of dot product?
What is the formula of dot product angle?
How to calculate dot product?
What is the difference between positive and negative dot products?
What happens when a dot product is 0?
What is the difference between dot product and cross product?
How to calculate matrix dot product?

About scalar product calculator

Finding out the dot product of vectors can be challenging. With this page, you can calculate dot products easily, and find all the essential information about dot products that you need to know.

How to use dot product calculator?

Add your vector coordinates to the dot product calculator, and you get a scalar result.
If you have 2-dimensional coordinates, add 0s' to z-coordinates and you can use the calculator for your vectors.

What is a dot product?

The dot product is a way to multiply vectors that result in scalar quantity. The dot product is also often referred to as a scalar product. The result of the dot product is dependent on the angle between the vectors and the lengths of the input.
Therefore dot product is a simple but fundamental concept that converts similarities between different vectors into a scalar result.
Dot product in math

What is the formula of dot product?

The dot product of two vectors that are defined as a and b are following:
a⋅b = |a| * |b| * cosθ

What is the formula of dot product angle?

The dot product angle formula for two vectors that are defined as a and b is following:
cosθ = a·b / (|a| * |b|)

How to calculate dot product?

The dot product between vectors is computed by estimating how many vectors are pointing in the same direction as one another.
Dot product calculation is simply done by multiplying vectors' respective coordinates and adding them up.
For two vectors a and b, dot product is calculated as following:
(a1 * b1) + (a2 * b2) + (a3 * b3) .... + (an * bn)

What is the difference between positive and negative dot products?

The quantity that gets given is relative to the two vectors' directions.
If the angle between them is lesser than 90 degrees, the dot product will be positive, and they are closer to being in similar directions.
If the angle between them is greater than 90 degrees, the dot product will be negative, and they are closer to being in opposite directions.
Positive and negative dot product

What happens when a dot product is 0?

If the two sides are perpendicular to each other at 90 degrees, the dot product is zero.

What is the difference between dot product and cross product?

The dot product of two vectors shows the magnitude of the two vectors and the cosine of the angle that they form with each other.
A cross product of two vectors is produced by the sine of angle that they form with each other and the magnitude of the two vectors.
The difference between a dot product and a cross product is that the former is a scalar quantity, while the latter is a vector quantity.
Therefore the result of the dot product is a single number and the result of the cross product is a vector.
Cross product

How to calculate matrix dot product?

To get the matrix dot product, the rows of the first matrices and columns of the second matrices have to have the same length.
Matrix multiplication

John Cruz
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

Dot Product Calculator English
Published: Tue Aug 24 2021
Latest update: Mon Oct 18 2021
In category Mathematical calculators
Add Dot Product Calculator to your own website