**Cosine similarity **measures the similarity between two vectors of an inner product space by calculating the cosine of the angle between the two vectors.

Python **Cosine similarity** is one of the most widely used and powerful similarity measures.

Use `dot() and norm() `

functions of python NumPy package to calculate `Cosine Similarity`

in python.

**Cosine Similarity** **Formula**

For two vectors, A and B, the Cosine Similarity in Python is calculated as:

**Cosine Similarity** = ΣA_{i}B_{i} / (√ΣA_{i}^{2}√ΣB_{i}^{2})

In this article, we will discuss **how to calculate cosine similarity in python** and cosine similarity examples.

**Cool Tip:** Learn how to calculate mean squared error (MSE) in python!

## Using Numpy for Cosine Similarity

We will be using `numpy `

library available in python to calculate **cosine similarity** between two vectors.

If you don’t have `numpy`

library installed then use the below command on the windows command prompt for NumPy library installation

pip install numpy

Let’s understand with examples about how to **calculate Cosine similarity** in python with given below python code

## Calculate Cosine Similarity in Python

lets assume we have data as below;- x = [1, 1, 1, 1, 0, 0, 0, 0, 0] y = [0, 0, 1, 1, 1, 1, 0, 0, 0]

Using `numpy.array()function we will create x & y arrays of the `

same length.

#import modules import numpy as np from numpy import dot from numpy.linalg import norm #define arrays x = np.array([1, 1, 1, 1, 0, 0, 0, 0, 0]) y = np.array([0, 0, 1, 1, 1, 1, 0, 0, 0]) #calculate Cosine Similarity python result = dot(x, y)/(norm(x)*norm(y)) print("The Cosine Similarity between two vectors is: ",result)

In the above code, we import `numpy`

package to use `dot() and norm() `

functions to calculate `Cosine Similarity`

in python.

Using `dot(x, y)/(norm(x)*norm(y))`

, we calculate the cosine similarity between two vectors x & y in python.

The output of the above **cosine similarity in python** code :

//Output The Cosine Similarity between two vectors is: 0.5

**Cool Tip:** Check here article on how to calculate MAPE in python!

## Calculate Cosine Similarity between arrays of same length in Python

In this example, we will calculate** Python Cosine similarity** between two randomly generated arrays of the same length in python with the given below code.

#import modules import numpy as np from numpy import dot from numpy.linalg import norm #define arrays x = np.random.randint(10, size=100) y = np.random.randint(10, size=100) # Calculate Cosine Similarity Python result = dot(x, y)/(norm(x)*norm(y)) print("The Cosine Similarity between two vectors is: ",result)

In the above code using `numpy.random.randint()`

, we create two random arrays of size 100.

Using `dot(x, y)/(norm(x)*norm(y))`

we calculate the **cosine similarity** between two vectors x & y in Python.

The output of the above **cosine similarity in python code**.

#output The Cosine Similarity between two vectors is: 0.6373168018459651

**Cool Tip:** Learn how to calculate SMAPE in python!

## Calculate Cosine Similarity between arrays of different length in Python

In this example, we will calculate** Cosine similarity** Python between two randomly generated arrays of different lengths in python with the given below code.

import numpy as np from numpy import dot from numpy.linalg import norm #define arrays x = np.random.randint(10, size=90) #length=90 y = np.random.randint(10, size=100) #length=100 #calculate Cosine Similarity Python result = dot(x, y)/(norm(x)*norm(y)) print("The Cosine Similarity between two vectors is: ",result)

In the above code, it will raise the ValueError because the arrays are of different lengths.

**Note**:-** We are not able to calculate the cosine similarity between the arrays of different lengths.**

The Error of the above cosine similarity in python code is shown below.

#ERROR ValueError: shapes (90,) and (100,) not aligned: 90 (dim 0) != 100 (dim 0)

**Cool Tip:** Learn how to calculate Euclidean distance in python!

## Conclusion

I hope, you may find **how to calculate Cosine Similarity in python tutorial with step by step illustration of cosine similarity examples educational and helpful. **

Using **NumPy** package in Python, cosine similarity can be calculated using dot() and norm() functions.