*60*

This tutorial explains how to calculate the dot product in Excel.

**What is the Dot Product?**

Given vector *a* = [a_{1}, a_{2}, a_{3}] and vector *b* = [b_{1}, b_{2}, b_{3}], theÂ **dot product**Â of vector a and vector b, denoted asÂ **a Â· b**, is given by:

**a Â· b**Â = a_{1}Â * b_{1}Â + a_{2}Â * b_{2}Â + a_{3}Â * b_{3}

For example, if *a* = [2, 5, 6] and *b* = [4, 3, 2], then the dot product of *a* and *b* would be equal to:

**a Â· b =Â **2*4 + 5*3 + 6*2

**a Â· b =Â **8 + 15 + 12

**a Â· b =Â **35

In essence, theÂ **dot productÂ **is the sum of the products of the corresponding entries in two vectors.

**How to Find the Dot Product in Excel**

To find the dot product of two vectors in Excel, we can use the followings steps:

**1. Enter the data**. Enter theÂ data values for each vector in their own columns. For example, enter the data values for vector *a* = [2, 5, 6] into column A and the data values for vector *b* = [4, 3, 2] into column B:

**2. Calculate the dot product.** To calculate the dot product, we can use the Excel functionÂ **SUMPRODUCT()**, which uses the following syntax:

**SUMPRODUCT(array1, [array2], â€¦)**

**arrayÂ**â€“ the first array or range to multiply, then add.**array2Â**â€“ the second array or range to multiply, then add.

In this example, we can type the following into cell **D1** to calculate the dot product between vector *a* and vector* b*:

**=SUMPRODUCT(A1:A3, B1:B3)**

This produces the valueÂ **35**, which matches the answer we got by hand.

Note that we can useÂ **SUMPRODUCT()Â **to find the dot product for any length of vectors. For example, suppose vectorÂ *aÂ *andÂ *bÂ *were both of length 20. Then we could enter the following formula in cell **D1Â **to calculate their dot product:

**=SUMPRODUCT(A1:A20, B1:B20)**

**Potential Errors in Calculating the Dot Product**

The functionÂ **SUMPRODUCT()Â **will return a **#VALUE!** error if the vectors do not have equal length.

For example, if vector *a* has length 20 and vector *b* has length 19, then the formula **=SUMPRODUCT(A1:A20, B1:B19)** will return an error.

The two vectors need to have the same length in order for the dot product to be calculated.

**Additional Resources**

The following tutorials explain how to calculate a dot product in different statistical software:

How to Calculate the Dot Product in Google Sheets

How to Calculate the Dot Product in R

How to Calculate a Dot Product on a TI-84 Calculator