# How to Compute Euclidean Distance in Python

Euclidean Distance is one of the most used distance metrics in Machine Learning. In this article, we will discuss Euclidean Distance, how to derive formula, implementation in python and finally how it differs from Manhattan Distance.

Different machine learning algorithm, whether they are supervised or unsupervised, uses distance metrics to find the pattern in the input data. It helps to improve the performance of the machine learning models despite its classification or clustering tasks. Different distances metrics are available to calculate the distance between the input data, such as Manhattan Distance, Euclidean, Minkowski, and Hamming Distance. In the previous article, we discussed all about Manhattan Distance Metrics. This article will discuss the next distance metric, Euclidean Distance Metric.

**Also Read:** Evaluating a Machine Learning Algorithm

**Also Read:** Difference Between Supervised and Unsupervised Learning

So, let’s dive deep to learn more about Euclidean Distance Metric.

**Table of Content**

- What is Euclidean Distance
- Euclidean Distance Formula
- Euclidean Distance Python
- Difference between Euclidean Distance and Manhattan Distance

**What is Euclidean Distance**

Euclidean Distance Metric is one of the most used distance metrics in the machine learning algorithm. It gives the shortest distance between two points.

The distance between two points in either the plane or 3-D space measures the length of the segment between two points.

- The distance between two points in either the plane or 3-D space measures the length of the segment between two points.
- They are generally used to calculate the distance between two rows of data that have numerical values (Integer or Decimal Values).
- KNN- classifier uses a Euclidean metric to classify the unknown instances by calculating the distance between the points in the training set.
- The value of the Euclidean distance will be greater than or equal to zero.
- If the value of the Euclidean Distance is Equal to zero, it implies that both the points are equivalent; else, they are different from each other.

Till now, we have learned about what is Euclidean distance metric and where it is used. Now, we will learn how to calculate the distance using it.

**Euclidean Distance Formula**

The Euclidean distance formula can be easily derived using the Pythagoras theorem.

Pythagoras’ Theorem states:

“In a right-angle triangle, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.”

Now, we will calculate the Euclidean distance using the Pythagoras Formula:

Let’s take any two points (A, B) on a line segment that have coordinates A* (x _{1}, y_{1})*, and B

*(x*, where

_{2}, y_{2})*(x*are the points on the

_{1}, x_{2})*x*-axis and

*(y*are the points on

_{1}, y_{2})*y*-axis.

Now, using these two points, draw a right-angle triangle, having the right angle at O, So the distance between

AO = (x_{2} – x_{1})

BO = (y_{2} – y_{1})

Now, using the Pythagoras Theorem, we will get the euclidean distance between two points (here AB), i.e.,

Hence, the euclidean distance between two points is:

The general formula of Euclidean Distance metric in *n*-dimension space is given by:

Where,

** n**: number of dimensions

** (pi, qi)**: data points

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Now, let’s have some examples to get a clear understanding of Euclidean Distance Metric:

**Euclidean Distance Python**

Here, we will discuss, two approaches to calculate the distance using python:

**Method – 1:** **Using Dot and Square Root Method** **(Formula)**

#using Formula# Import NumPy Libraryimport numpy as np
# initializing points in numpy arrays
P1 = np.array((9, 16, 25))P2 = np.array((1, 4, 9))
# subtracting both the vectors
temp = P1 - P2
# Using Formula
euclid_dist = np.sqrt(np.dot(temp.T, temp))
# printing Euclidean distanceprint(euclid_dist)

**Output**

21.540659

**Method – 2: Using Sci-Py Library**

# using distance.euclidean() method# Import SciPi Library
from scipy.spatial import distance# define the points
P1 = (9, 16, 25)P2 = (1, 4, 9)
# print Euclidean distance print(distance.euclidean(P1,P2))

**Output**

21.540659

**Euclidean Distance vs. Manhattan Distance**

Parameter |
Euclidean Distance |
Manhattan Distance |

Definition |
It is the length of the line segment joining a given pair of points. | It is the sum of the distance at each point. |

Uniqueness |
It is unique and the shortest distance between two points. | There may be many Manhattan paths between two points. |

Use |
It is mainly used in the KNN algorithm. | It is used in Linear regression with Ridge Regularization. |

Formula |

**Also Read:** Lasso Regression vs Ridge Regression

**Conclusion**

Euclidean Distance is one of the most used distance metrics in Machine Learning. In this article, we will discuss Euclidean Distance, how to derive formula, implementation in python and finally how it differs from Manhattan Distance.

Hope this article helped you to learn more about Euclidean Distance.

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## FAQs on How to Compute Euclidean Distance in Python

**How can I compute the Euclidean distance between two points in 2D space using basic Python?**

You can use the formula for Euclidean distance, which is the square root of the sum of the squared differences between corresponding coordinates.

import math

def euclidean_distance_2d(point1, point2):

return math.sqrt((point1[0] - point2[0])**2 + (point1[1] - point2[1])**2)

# Example usage

point1 = (1, 2)

point2 = (4, 6)

print(euclidean_distance_2d(point1, point2)) # Output: 5.0

**How can I compute the Euclidean distance between two points in N-dimensional space using NumPy?**

NumPy provides efficient array operations that can be used to compute the Euclidean distance.

import numpy as np

def euclidean_distance_numpy(point1, point2):

return np.linalg.norm(np.array(point1) - np.array(point2))

# Example usage

point1 = [1, 2, 3]

point2 = [4, 5, 6]

print(euclidean_distance_numpy(point1, point2)) # Output: 5.196152422706632

**How can I compute the Euclidean distance between two points using the SciPy library?**

from scipy.spatial.distance import euclidean

# Example usage

point1 = [1, 2, 3]

point2 = [4, 5, 6]

print(euclidean(point1, point2)) # Output: 5.196152422706632

**How can I compute the Euclidean distance between two points using a custom function in Python?**

def euclidean_distance_custom(point1, point2):

squared_diff = [(a - b) ** 2 for a, b in zip(point1, point2)]

return sum(squared_diff) ** 0.5

# Example usage

point1 = [1, 2, 3]

point2 = [4, 5, 6]

print(euclidean_distance_custom(point1, point2)) # Output: 5.196152422706632

**How can I compute the Euclidean distance between multiple pairs of points in a dataset using Pandas?**

Pandas can be used in combination with NumPy to compute the Euclidean distance for multiple pairs of points in a DataFrame.

import pandas as pd

import numpy as np

def euclidean_distance_pandas(df, point1_col, point2_col):

return np.linalg.norm(df[point1_col] - df[point2_col], axis=1)

# Example usage

data = {

'point1': [[1, 2], [3, 4]],

'point2': [[4, 6], [7, 8]]

}

df = pd.DataFrame(data)

df[['point1_x', 'point1_y']] = pd.DataFrame(df['point1'].tolist(), index=df.index)

df[['point2_x', 'point2_y']] = pd.DataFrame(df['point2'].tolist(), index=df.index)

print(euclidean_distance_pandas(df[['point1_x', 'point1_y']], df[['point2_x', 'point2_y']])) # Output: [5. 5.65685425]

**About the Author**

Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio