The **Hamming distance** between two vectors is simply the sum of corresponding elements that differ between the vectors.

For example, suppose we have the following two vectors:

x = [1, 2, 3, 4] y = [1, 2, 5, 7]

The Hamming distance between the two vectors would be **2**, since this is the total number of corresponding elements that have different values.

To calculate the Hamming distance between two columns in Excel, we can use the following syntax:

=COUNT(RANGE1)-SUMPRODUCT(--(RANGE1 = RANGE2))

Here’s what the formula does in a nutshell:

**COUNT**finds the total number of observations in the first column.**RANGE1 = RANGE2**compares each pairwise observations between the columns and returns a TRUE or FALSE.**– –**converts TRUE and FALSE values to 0 and 1.**SUMPRODUCT**finds the sum of all 1’s.

This tutorial provides several examples of how to use this calculation in practice.

**Example 1: Hamming Distance Between Binary Vectors**

The following code shows how to calculate the Hamming distance between two columns in Excel that each contain only two possible values:

The Hamming distance between the two columns is **3**.

**Example 2: Hamming Distance Between Numerical Vectors**

The following code shows how to calculate the Hamming distance between two columns in Excel that each contain several numerical values:

** **

The Hamming distance between the two vectors is **7**.

**Additional Resources**

How to Calculate the Mean Absolute Deviation in Excel

How to Normalize Data in Excel

How to Find Outliers in Excel