*17*

The **Euclidean distance** between two vectors, A and B, is calculated as:

**Euclidean distance = âˆšÎ£(A _{i}-B_{i})^{2}**

To calculate the Euclidean distance between two vectors in R, we can define the following function:

euclidean function(a, b) sqrt(sum((a - b)^2))

We can then use this function to find the Euclidean distance between any two vectors:

#define two vectors a #calculate Euclidean distance between vectors euclidean(a, b) [1] 12.40967

The Euclidean distance between the two vectors turns out to beÂ **12.40967**.

Note that we can also use this function to calculate the Euclidean distance between two columns of a data frame:

#define data frame df #calculate Euclidean distance between columnsaanddeuclidean(df$a, df$d) [1] 7.937254

Note that this function will produce a warning message if the two vectors are not of equal length:

#define two vectors of unequal length a #attempt to calculate Euclidean distance between vectors euclidean(a, b) [1] 23.93742 Warning message: In a - b : longer object length is not a multiple of shorter object length

*You can refer to this Wikipedia page to learn more details about Euclidean distance.*

**Additional Resources**

How to Calculate Manhattan Distance in R

How to Calculate Minkowski Distance in R

How to Calculate Hamming Distance in R

How to Calculate Mahalanobis Distance in R

How to Calculate Levenshtein Distance in R