Using RMSE in Python
 the Formula for Root Mean Square Error in Python

Calculate
RMSE
UsingNumPy
in Python 
Calculate
RMSE
Usingscikitlearn
Library in Python
RMS (root mean square
), also known as the quadratic mean, is the square root of the arithmetic mean of the squares of a series of numbers.
RMSE
(root mean square error
) gives us the difference between actual results and our calculated results from the model. It defines the quality of our model (which uses quantitative data), how accurate our model has predicted, or the percentage of error in our model.
RMSE
is one of the methods for evaluating supervised machine learning models. The larger the RMSE
will be the inaccuracy of our model and vice versa.
There are multiple ways to find the RMSE
in Python by using the NumPy
library or scikitlearn
library.
the Formula for Root Mean Square Error in Python
The logic behind calculating the RMSE
is through its following formula:
Calculate RMSE
Using NumPy
in Python
NumPy
is a useful library for dealing with large data, numbers, arrays, and mathematical functions.
Using this library, we can easily calculate RMSE
when given the actual
and predicted
values as an input. We will use the builtin functions of the NumPy
library for performing different mathematical operations like square, mean, difference, and square root.
In the following example, we will calculate RMSE
by first calculating the difference
between actual
and predicted
values. We calculate the square
of that difference, then take the mean
.
Until this step, we will get the MSE
. To get the RMSE
, we will take the square root
of MSE
.
To use this library, we should install it first.
Example Code:
#python 3.x
import numpy as np
actual = [1,2,5,2,7, 5]
predicted = [1,4,2,9,8,6]
diff=np.subtract(actual,predicted)
square=np.square(diff)
MSE=square.mean()
RMSE=np.sqrt(MSE)
print("Root Mean Square Error:", RMSE)
Output:
#python 3.x
Root Mean Square Error: 3.265986323710904
Calculate RMSE
Using scikitlearn
Library in Python
Another way to calculate RMSE
in Python is by using the scikitlearn
library.
scikitlearn
is useful for machine learning. This library contains a module called sklearn.metrics
containing the builtin mean_square_error
function.
We will import the function from this module into our code and pass the actual
and predicted
values from the function call. The function will return the MSE
. To calculate the RMSE
, we will take MSE
’s square root.
To use this library, we should install it first.
Example Code:
#python 3.x
from sklearn.metrics import mean_squared_error
import math
actual = [1,2,5,2,7, 5]
predicted = [1,4,2,9,8,6]
MSE = mean_squared_error(actual, predicted)
RMSE = math.sqrt(MSE)
print("Root Mean Square Error:",RMSE)
Output:
#python 3.x
Root Mean Square Error: 3.265986323710904