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In the world of mathematics, the shortest distance between two points in any dimension is called the Euclidean distance. It is the square root of the sum of the squares of the differences between the two points.

In Python, the numpy, scipy modules are equipped with functions to perform mathematical operations and calculate the line segment between two points.

In this tutorial, we will discuss different ways to calculate the Euclidean distance between coordinates.

Find the Euclidean distance between two points using NumPy module

When the coordinates are in the form of arrays, you can use the numpy module to find the required distance. It has norm()a function that returns the vector norm of an array. It can help calculate the Euclidean distance between two coordinates as shown below.

import numpy as np

a = np.array((1, 2, 3))
b = np.array((4, 5, 6))

dist = np.linalg.norm(a - b)

print(dist)

Output:

5.196152422706632

We can also implement the mathematical formula directly using the numpy module. For this method, we will use numpy.sum()the function, which returns the sum of the elements, and numpy.square()the function, which returns the square of the elements.

import numpy as np

a = np.array((1, 2, 3))
b = np.array((4, 5, 6))

dist = np.sqrt(np.sum(np.square(a - b)))

print(dist)

Output:

5.196152422706632

numpy.sqrt()The function returns the square root of a value.

Another way to implement the Euclidean distance formula is to use dot()the function. We can find the dot product of the difference and its transpose, returning the sum of the squares.

For example,

import numpy as np

a = np.array((1, 2, 3))
b = np.array((4, 5, 6))

temp = a - b
dist = np.sqrt(np.dot(temp.T, temp))

print(dist)

Output:

5.196152422706632

Use distance.euclidean()the function to find the Euclidean distance between two points

We discussed different ways to calculate Euclidean distance using the numpy module. However, these methods can be a bit slow, so there are faster alternatives.

The scipy library has many functions for mathematical and scientific computing. distance.euclidean()The function returns the Euclidean distance between two points.

For example,

from scipy.spatial import distance

a = (1, 2, 3)
b = (4, 5, 6)

print(distance.euclidean(a, b))

Output:

5.196152422706632

Use math.dist()the function to find the Euclidean distance between two points

mathThe module can also be used as an alternative. The module's dist()function can return a line segment between two points.

For example,

from math import dist

a = (1, 2, 3)
b = (4, 5, 6)

print(dist(a, b))

Output:

5.196152422706632

scipyThe and mathmodule methods are NumPyfaster alternatives to the methods and can be used when the coordinates are in the form of tuples or lists.