The **root mean squared error** (**RMSE**) is used to measured the differences between values predicted by the model and observed values of the model.

The root mean squared error (**RMSE**) is always non-negative, RMSE value near to 0 indicates a perfect fit to the data.

**Root mean squared error** or Root mean squared deviation (**RMSD**) is the square root of the average of squared errors. RMSD is measure of accuracy to compare forecasting errors of different models for a particular dataset.

In this tutorial, we will discuss about how to calculate **root mean squared error** (RMSE) in python.

## RMSE Formula

The root mean squared error (**RMSE**) is defined as follows:

Where,

n = sample data points

y = predictive value for the j^{th} observation

y^ = observed value for j^{th} observation

For an unbiased estimator, **RMSD **is square root of variance also known as standard deviation. **RMSE **is the good measure for *standard deviation* of the typical observed values from our predicted model.

We will be using `sklearn.metrics`

library available in python to calculate mean squared error, later we can simply use `math `

library to square root of mean squared error value.

We will be using `numpy `

library to generate actual and predication array.

## pip install numpy

If you don’t have `numpy `

package installed on your system, use below command in command prompt

pip install numpy

## pip install sklearn

If you don’t have `sklearn `

package installed on your system, use below commands in command prompt

pip install sklearn

## How to Calculate RMSE in Python

Lets understand with examples about how to **calculate RMSE** in python with given below python code

from sklearn.metrics import mean_squared_error from math import sqrt import numpy as np #define Actual and Predicted Array actual = np.array([10,11,12,12,14,18,20]) pred = np.array([9,10,13,14,17,16,18]) #Calculate RMSE result = sqrt(mean_squared_error(actual,pred)) # Print the result print("RMSE:", result)

In the above example, we have created actual and prediction array with the help of `numpy `

package array function.

We then use `mean_squared_error()`

function of `sklearn.metrics`

library which take actual and prediction array as input value. It returns mean squared error value.

Later, we find **RMSE **value using square root of mean squared error value.

Above code returns **root mean squared error** (RMSE) value for given actual and prediction model is 1.85164

Lets check out root mean squared value (*RMSE*) calculation with few more examples.

## Example 1 – RMSE Calculation

Lets assume, we have actual and predicted dataset as follows

actual = [4,7,3,9,12,8,14,10,12,12]

prediction = [5,7,3,8,10,8,12,11,11,13]

Calculate RMSE for given model.

Here, again we will be using `numpy `

package to create actual and prediction array and `mean_squared_error()`

funciton of `sklearn.metrics`

library for **RMSE **calculation in python.

Python code is given as below

from sklearn.metrics import mean_squared_error from math import sqrt import numpy as np #define Actual and Predicted Array actual = np.array([4,7,3,9,12,8,14,10,12,12]) pred = np.array([5,7,3,8,10,8,12,11,11,13]) #Calculate RMSE result = sqrt(mean_squared_error(actual,pred)) # Print the result print("RMSE:", result)

Above code returns root mean squared (**RMSE**) for given actual and prediction dataset is 1.14017

## Example 2 – RMSE Calculation

Lets assume, we have actual and predicted dataset as follows

actual = [14,17,13,19,12,18,14,10,12,12]

prediction = [15,14,14,18,10,16,12,11,11,13]

Calculate RMSE for given model.

Here, again we will be using `numpy `

package to create actual and prediction array and `mean_squared_error() `

funciton of `sklearn.metrics`

library for **RMSE **calculation in python.

Python code is given as below

from sklearn.metrics import mean_squared_error from math import sqrt import numpy as np #define Actual and Predicted Array actual = np.array([14,17,13,19,12,18,14,10,12,12]) pred = np.array([15,14,14,18,10,16,12,11,11,13]) #Calculate RMSE result = sqrt(mean_squared_error(actual,pred)) # Print the result print("RMSE:", result)

Above code returns root mean squared (**RMSE**) for given actual and prediction dataset is 1.643167

## Conclusion

I hope, you may find how to calculate **root mean square** (RMSE) in python tutorial with step by step illustration of examples educational and helpful.

**RMSE **is mostly used to find model fitness for given dataset. If *RMSE *has value 0, it means that its perfect fit as there is no difference in predicted and observed values.