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. Letâ€™s see the methods below.

**Table of Contents**hide

## Download Practice Workbook

Download the practice workbook from here.

## 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.

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

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, letâ€™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. Letâ€™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**.

**đź”Ž**** 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 the 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.

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### 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** and 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 **square 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.

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### 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**.

**đź”Ž**** 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.

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## 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. Follow our website **ExcelDemy** to get more articles like this.

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