# Use Euler's Number in Python

Rayven Esplanada Jan 30, 2023 Apr 23, 2021

Euler’s number or `e` is one of the most fundamental constants in mathematics, much like `pi`. `e` is the base of natural logarithmic functions. It is an irrational number representing the exponential constant.

This tutorial will demonstrate how to replicate the Euler’s number (`e`) in Python.

There are three common ways to get the euler’s number and use it for an equation in Python.

## Use `math.e` to Get Euler’s Number in Python

The Python module `math` contains a number of mathematical constants that can be used for equations. Euler’s number or `e` is one of those constants that the `math` module has.

``````from math import e
print(e)
``````

Output:

``````2.718281828459045
``````

The output above is the base value of the `e` constant.

As an example equation, let’s create a function get the value of `e^n` or `e` to the power of a number `n` where `n = 3`.

Also, note that the syntax for the power operation in Python is double asterisks `**`.

``````from math import e

def getExp(n):
return e**n

print(getExp(3))
``````

Output:

``````20.085536923187664
``````

If you prefer to have control over the number of decimal places the result has, a way to achieve this is by formatting the value as a string and printing it out after formatting it.

To format a float value to `n` decimal places, we can use the `format()` function over a string with this syntax `{:.nf}` where `n` is the number of decimal places to be displayed.

For example, using the same example above, format the output to 5 decimal places.

``````def getExp(n):
return "{:.5f}".format(e**n);

print(getExp(3))
``````

Output:

``````20.08554
``````

## Use `math.exp()` to Get Euler’s Number in Python

The module `math` also has a function called `exp()` that returns the value of `e` to the power of the number. Compared to `math.e`, the `exp()` function performs considerably faster and includes code that validates the given number parameter.

For this example, try using a decimal number as a parameter.

``````import math

print(math.exp(7.13))
``````

Output:

``````1248.8769669132553
``````

Another example would be getting the actual base value of `e` by setting the parameter to `1` to determine the value.

``````import math

print(math.exp(1))
``````

Output:

``````2.718281828459045
``````

The output is the actual value of `e` set to 15 decimal places.

## Use `numpy.exp()` to Get Euler’s Number in Python

The `exp()` function within the `NumPy` module also does the same operation and accepts the same parameter as `math.exp()`.

The difference is that it performs faster than both `math.e` and `math.exp()` and while `math.exp()` only accepts scalar numbers, `numpy.exp()` accepts scalar numbers as well as vectors such as arrays and collections.

For example, use the `numpy.exp()` function to accept both an array of floating-point numbers and a single integer value.

``````import numpy as np

int arr = [3., 5.9, 6.52, 7.13]
int singleVal = 2

print(np.exp(arr))
print(np.exp(singleVal))
``````

Output:

``````[20.08553692  365.03746787  678.57838534 1248.87696691]
7.38905609893065
``````

If an array of numbers is used as a parameter, then it will return back an array of results of the `e` constant raised to the power of all the values within the given array. If a single number is given as a parameter, then it will behave exactly like `math.exp()`.

In summary, to get the Euler’s number or `e` in Python, use `math.e`. Using `math.exp()` will need a number as a parameter to serve as the exponent value and `e` as its base value.

Using `exp()` in calculating the exponent of `e` over double asterisks, `**` performs better than the latter, so if you are dealing with huge numbers, then it’s better to use `math.exp()`.

Another option is to use `numpy.exp()`, which supports an array of numbers as a parameter and performs faster than both the solutions from the `math` module. So if vectors are involved within the equation, use `numpy.exp()` instead.

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