How to Calculate Cosine Similarity in Excel


Cosine Similarity is a measure of the similarity between two vectors of an inner product space.

For two vectors, A and B, the Cosine Similarity is calculated as:

Cosine Similarity = ΣAiBi / (√ΣAi2√ΣBi2)

This tutorial explains how to calculate the Cosine Similarity between vectors in Excel.

Cosine Similarity Between Two Vectors in Excel

Suppose we have the following two vectors in Excel:

We can use the following formula to calculate the Cosine Similarity between the two vectors in Excel:

=SUMPRODUCT(A$2:A$9,B2:B9)/(SQRT(SUMSQ(B2:B9))*SQRT(SUMSQ($A$2:$A$9)))

The following screenshot shows how to use this formula:

cosine similarity formula in Excel

The Cosine Similarity between the two vectors turns out to be 0.965195.

Note that we interpret the value for Cosine Similarity as follows:

  • A value of -1 indicates maximum dissimilarity
  • A value of 0 indicates that the two vectors are orthogonal
  • A value of 1 indicates maximum similarity

A value of 0.965195 indicates a high level of similarity between the two vectors in our example.

Additional Resources

The following tutorials explain how to calculate Cosine Similarity in other statistical software:

For an in-depth explanation of Cosine Similarity, refer to the following Wikipedia article:

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