When comparing two data sets, we employ root mean square error in a variety of applications. Moreover, the root mean square error is one of the most used statistics in GIS. This article will guide you to calculate the root mean square error in Excel with some easy and quick methods. Let’s see the methods below.

## Introduction to Root Mean Square Error (RMSE)

The Root Mean Square Error (RMSE) calculates the amount of error between 2 datasets. That means, it compares a predicted value to an observed or known value. Hence, the lower the RMSE, the closer the anticipated and observed values are.

## How to Calculate Root Mean Square Error in Excel: 3 Quick Methods

In this article, we will discuss **3** quick methods to calculate the root mean square error in Excel. Furthermore, we have used some excellent examples with explanations for a better understanding of the methods. Here, we have used a dataset (**B4:C8**) like the screenshot below which contains some Expected and Real values. Now, we need to calculate the root mean square error of them. So, without further delay, let’s get started.

### 1. Apply SUMSQ Function to Calculate Root Mean Square Error in Excel

#### 1.1 First Scenario

In the first method, we will apply **the SUMSQ function** in Excel to calculate the **root mean square error**. Here, we have used a combined formula that contains the **COUNTA** function and the **SQRT **function also. The **SUMSQ** function in Excel finds the sum of the squares of a set of numbers. Let’s see the steps below to use this function for calculating the **root mean square error** in Excel.

**Steps:**

- First, select cell
**C10**. - Secondly, to get the
**root mean square error**, type the formula:

`=SQRT(SUMSQ(B5:B8-C5:C8)/COUNTA(B5:B8))`

Here, the range **B5:B8** indicates the **Expected Values** and **C5:C8** indicates the **Real Values**.

**🔎**** How Does the Formula Work?**

**SUMSQ(B5:B8-C5:C8)**

This will first square the differences between the **Expected **and **Real Values** and then calculate their sum.

**COUNTA(B5:B8)**

It counts the number of non-empty cells in the **B5:B8** range.

**SQRT(SUMSQ(B5:B8-C5:C8)/COUNTA(B5:B8))**

This will calculate the square root of the whole calculation.

- Finally, press the
**Ctrl**+**Shift**+**Enter**keys and you will get the result like the screenshot below.

#### 1.2 Second Scenario

The dataset (**B4:C8**) below contains some **Expected Values** (**B5:B8**) and **Real Values** (**C5:C8**). Here, we will learn to find the **root mean square error** from the differences between **Expected** and **Real Values** using the **SUMSQ** function. The steps are below.

**Steps:**

- In the beginning, we need to find the differences between the
**Expected**and**Real Values**. For this, select the cell**D5**and type the formula:

`=B5-C5`

- After pressing
**Enter**, we will get the value of the difference in cell**D5**. - Thereupon, to get all the differences, drag the
**fill handle**.

- In this way, we have got all the differences.
- Now, select the cell
**C10,**and to find the**root mean square error**, type the formula in the cell:

`=SQRT(SUMSQ(D5:D8)/COUNTA(D5:D8))`

In this formula, the range **D5:D8** refers to the differences between **Expected **and **Real Values**. The **SUMSQ** function will square the differences between the **Expected **and **Real Values**. The **COUNTA** function will count the non-empty cells of the selected range and finally, the **SQRT **function will calculate the square root of the whole calculation.

- In the end, click the
**Ctrl**+**Shift**+**Enter**button to get the value of the**root mean square error (RMSE)**. We can see the final result in the screenshot below.

**Read More: **How to Calculate Mean Squared Error in Excel

### 2. Find Root Mean Square Error Using Excel AVERAGE Function

You may also use the **AVERAGE **function in Excel to determine the **root mean square error**. To acquire the difference between the **Expected Values** and the **Real Values** as shown in the picture below, first, follow the instructions in the way indicated in the **SUMSQ** function method above. Now, we need to calculate the square of the differences then the **Mean Square Error (MSE),** and finally the **Root Mean Square Error (RMSE)**. The steps to do so are below.

**Steps:**

- Firstly, to calculate the square of the difference, type the formula in the cell
**E5**:

`=D5^2`

- After pressing
**Enter**, we will get the result.

- Eventually, drag the
**fill handle**to find the square for all the difference values.

- As a result, we have got all the results.
- At this time, to find the
**mean square error**(**MSE**) using the**Average**function type the formula in cell**C10**:

`=AVERAGE(E5:E8)`

Here, the range **E5:E8** indicates the **sq**uare of the difference values.

- Subsequently, press the
**Enter**key to get the result.

- Therefore, to calculate the
**root mean square error**, type the formula in cell**C11**:

`=SQRT(C10)`

Here, **C10** denotes the **mean square error** (**MSE**) value.

- Lastly, press the
**Enter**button to find the result.

### 3. Root Mean Square Error Calculation with Excel RMSE Formula

Utilizing the Excel **RMSE** formula is another way to determine the root mean square error (RMSE) of a dataset. This combined formula contains the **SQRT** function, the **SUM **function, and the **COUNT **function respectively. For this method, first, calculate the square of the difference values by following method **2**. The steps for calculating the **root mean square error** using the** RMSE **formula are below.

- To calculate the
**RMSE**type the formula in cell**C10**:

`=SQRT(SUM(E5:E8)/COUNT(E5:E8))`

In the formula, the range **E5:E8** indicates the squares of the differences.

**🔎**** How Does the Formula Work?**

**SUM(E5:E8)**

It sums up the values in the range **E5:E8**.

**COUNT(E5:E8)**

This counts the number of cells in the range **E5:E8**.

**SQRT(SUM(E5:E8)/COUNT(E5:E8))**

It calculates the square root of the whole calculation.

- Lastly, click
**Ctrl**+**Shift**+**Enter**to get the result.

**Download Practice Workbook**

Download the practice workbook from here.

## Conclusion

I hope the above methods will be helpful for you to calculate root mean square error in Excel. Download the practice workbook and give it a try. Let us know your feedback in the comment section.

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