# Calculate Pi with Python

• Last Updated : 19 May, 2021

Pi is an irrational number having non-recurring decimal values. We commonly know Pi=3.14 or Pi=22/7, but it is just an approximation for our ease. There are two methods to calculate the value of pi in python:

Method 1: Using Leibniz’s formula

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The formula is – This series is never-ending, the more the terms this series contains, the closer the value of X converges to Pi value.

Approach:

• Initialize k=1 // this variable will be used as the denominator of leibniz’s formula, it will be incremented by 2
• Initialize sum=0 // sum will add all the elements of the series
• Run a for loop from 0 to 1000000 //at this value, we get the most accurate value of Pi
• Inside for loop, check if i%2==0 then do sum=sum+4/k
• Else, do sum=sum-4/k
• Increment k by 2, go to step 3

Below is the implementation:

## Python3

 `# Initialize denominator``k ``=` `1` `# Initialize sum``s ``=` `0` `for` `i ``in` `range``(``1000000``):` `    ``# even index elements are positive``    ``if` `i ``%` `2` `=``=` `0``:``        ``s ``+` `=` `4``/``k``    ``else``:` `        ``# odd index elements are negative``        ``s ``-``=` `4``/``k` `    ``# denominator is odd``    ``k ``+``=` `2``    ` `print``(s)`

Output:

`3.1415916535897743`

Method 2: Using acos() methods.

Approach:

1. The value of Π is calculated using acos() function which returns a numeric value between [-Π, Π].
2. Since using acos(0.0) will return the value for 2*Π. Therefore to get the value of Π:
` pi = round(2*acos(0.0));`

Below is the implementation:

## Python3

 `# Python3 program to calculate the``# value of pi up to 3 decimal places``from` `math ``import` `acos` `# Function that prints the``# value of pi upto N``# decimal places``def` `printValueOfPi():` `    ``# Find value of pi upto 3 places``    ``# using acos() function``    ``pi ``=` `round``(``2` `*` `acos(``0.0``), ``3``)` `    ``# Print value of pi upto``    ``# N decimal places``    ``print``(pi)`  `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``# Function that prints``    ``# the value of pi``    ``printValueOfPi()`

Output:

`3.142`

Method 3: Using NumPy

In this method, we will use numpy.pi methods to calculate the pi value.

## Python3

 `import` `numpy` `print``( numpy.pi )`

Output:

`3.141592653589793`

Method 4: Using math module

Python has an inbuilt library named math we can simply import math and print the value of pi.

## Python3

 `import` `math` `print``( math.pi )`

Output:

`3.141592653589793`

My Personal Notes arrow_drop_up