The **Euclidean distance** between two points in either the plane or 3-dimensional space measures the length of a segment connecting the two points. It is the most obvious way of representing the distance between two points.

In this tutorial, we will discuss about how to calculate **Euclidean distance** in python

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**Euclidean Distance** Formula

The **Euclidean distance** between two vectors, P and Q, is calculated as:

**Euclidean distance = √Σ(P _{i}-Q_{i})^{2}**

## Numpy for **Euclidean Distance**

**Euclidean Distance**

We will be using numpy library available in python to calculate the Euclidean distance 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

## How to Calculate **Euclidean Distance** in python

**Euclidean Distance**

In python, the numpy library provides** linalg.norm**() function to calculate the Euclidean distance.

Let’s understand with examples about how to **calculate Euclidean distance** in python with given below python code.

## Example #1 Euclidean Distance Calculation

#import modules import numpy as np from numpy.linalg import norm #Define Vectors p = np.array([2, 3,4,2]) q = np.array([1,-2,1,3]) #Calculate Euclidean distance between the two vectors result = norm(p-q) print("The Euclidean distance between the two Vectors: ",result)

In the above example, we have created a p and q array of the same length using `numpy `

package `array`

function.

Python function norm() accepts p and q array as input parameters and returns the Euclidean distance as the result.

The above code gives Euclidean distance between the two Vectors for given p and q array is 6.0. The output of the above code as below.

//Output The Euclidean distance between the two Vectors: 6.0

## Example #2 Euclidean Distance Calculation

Let’s take another example to find Euclidean distance between two arrays of different length with given below python code.

#import modules import numpy as np from numpy.linalg import norm #Define Vectors p = np.random.randint(10, size=90) #length=90 q = np.random.randint(10, size=100) #length=100 #Calculate Euclidean distance between the two vectors result = norm(p-q) print("The Euclidean distance between the two Vectors: ",result)

In the above example, we have created a p and q array of the different lengths using numpy library’s random.randint() function.

In this case, python function norm() gives a warning message as two arrays are of different lengths as mentioned below.

//Output ValueError: operands could not be broadcast together with shapes (90,) (100,)

**NOTE**:- The norm() function is only applicable for arrays of same length.

## Example #3 Euclidean distance between columns in pandas dataframe in python

#import modules import pandas as pd from numpy.linalg import norm #define DataFrame with three columns df = pd.DataFrame({'examScore': [88, 85, 76, 70, 92, 94, 89, 85, 90, 93], 'studyHours': [4, 3, 6, 5, 4, 5, 8, 7, 4, 6], 'Grades': [82, 88, 75, 74, 93, 97, 83, 90, 90, 80]}) print(df) #calculate Euclidean distance between 'examScore' and 'Grades' result = norm(df['examScore'] - df['Grades']) print("Euclidean distance between 'examScore' and 'Grades': ",result)

Let’s consider a pandas Dataframe with 3 Columns i.e examScore, studyHours, Grades.

Calculate the Euclidean distance between ‘examScore’ and ‘Grades’ dataframe. The norm() functions gives the below output for the above code.

examScore studyHours Grades 0 88 4 82 1 85 3 88 2 76 6 75 3 70 5 74 4 92 4 93 5 94 5 97 6 89 8 83 7 85 7 90 8 90 4 90 9 93 6 80 Euclidean distance between 'examScore' and 'Grades': 17.378147196982766

Above code gives Euclidean distance between ‘examScore’ and ‘Grades’ is 17.378147.

## Conclusion

I hope you find the above article on how to calculate Euclidean distance between two points in python code useful and educational.