Last updated on August 5th, 2025
In mathematics, the Euclidean distance formula is used to calculate the straight-line distance between two points in Euclidean space. It is derived from the Pythagorean theorem and is applicable in various dimensions. In this topic, we will learn the formula for calculating Euclidean distance.
The Euclidean distance is a measure of the true straight line distance between two points in Euclidean space. Let's learn the formula to calculate the Euclidean distance.
The Euclidean distance between two points ((x1, y1)) and ((x2, y2)) in a two-dimensional plane is calculated using the formula: [ {Distance} = √{(x2 - x1)2 + (y2 - y1)2} ]
In three-dimensional space, the Euclidean distance between points ((x1, y1, z1)) and ((x2, y2, z2)) is calculated as: [ {Distance} = √{(x2 - x1)2 + (y2 - y1)2+ (z2 - z1)2}]
The Euclidean distance formula is crucial in various fields such as physics, computer science, and machine learning.
The Euclidean distance formula might seem complex at first, but it can be easily remembered with practice.
The Euclidean distance formula is widely used in various real-world applications:
There are common errors that people make while applying the Euclidean distance formula. Here are some mistakes and ways to avoid them.
Find the Euclidean distance between points (3, 4) and (7, 1).
The Euclidean distance is 5.
Using the formula: √{(7 - 3)2 + (1 - 4)2}
= √{(4)2 + (-3)2}
= √{16 + 9}
= √{25}
= 5
Calculate the distance between (2, -1, 3) and (5, 2, 6) in three-dimensional space.
The Euclidean distance is 5.
Using the formula:√{(5 - 2)2 + (2 -(-1)2+ (6 - 3)2 }
= √{(3)2 + (3)2+ (3)2}
= √{9 + 9+ 9}
= √{27}
= 5.2 { (approximately)}
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.