## Introduction to the Root Mean Square Error (RMSE)

The Root Mean Square Error (RMSE) calculates the amount of error between 2 datasets. 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 the Root Mean Square Error in Excel: 3 Quick Methods

We have a dataset (**B4:C8**) like the screenshot below which contains some Expected and Real values. We need to calculate the root mean square error of them.

### Method 1 – Apply the SUMSQ Function to Calculate the Root Mean Square Error in Excel

#### Case 1.1 – Using SQRT and COUNTA

**Steps:**

- Select cell
**C10**. - To get the
**root mean square error**, use 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.

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

#### Case 1.2 – Using a Helper Column

The dataset (**B4:C8**) below contains some **Expected Values** (**B5:B8**) and **Real Values** (**C5:C8**).

**Steps:**

- We need to find the differences between the
**Expected**and**Real Values**. For this, select the cell**D5**and use the formula:

`=B5-C5`

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

- Select the cell
**C10,**and use the following formula in the cell:

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

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.

- 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

### Method 2 – Find the Root Mean Square Error Using the AVERAGE Function

We calculated the differences between the **Expected Values** and the **Real Values** as shown in the picture below.

**Steps:**

- To calculate the square of the difference, use this formula in the cell
**E5**:

`=D5^2`

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

- Drag the
**fill handle**to find the square for all the difference values.

- To find the
**mean square error**(**MSE**) using the**Average**function, use this formula in cell**C10**:

`=AVERAGE(E5:E8)`

- Press the
**Enter**key to get the result.

- To calculate the
**root mean square error**, use this formula in cell**C11**:

`=SQRT(C10)`

- Press the
**Enter**key to find the result.

### Method 3 – Root Mean Square Error Calculation with Excel RMSE Formula

- Calculate the square of the difference values by following
**Method 2**.

- To calculate the
**RMSE,**use this formula in cell**C10**:

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

The range **E5:E8** indicates the squares of the differences.

** How Does the Formula Work?**

**SUM(E5:E8)**

Sums up the values in the range **E5:E8**.

**COUNT(E5:E8)**

Counts the number of cells in the range **E5:E8**.

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

Calculates the square root of the whole calculation.

- Click
**Ctrl**+**Shift**+**Enter**to get the result.

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