Calculate Pi with Python

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. In this article, we will see how to calculate PI with Python and also how to use PI in Python.

Calculate and Use PI in Python

Below are the ways by which we can calculate and use PI in Python:

• Using NumPy
• Using math module
• Using Leibniz's formula
• Using acos() methods
• Using Math.radians

Calculate PI in Python Using math module

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

import math

print( math.pi )

3.141592653589793

Finding PI Value Using NumPy

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

import numpy

print( numpy.pi )

 Output

3.141592653589793

Calculate PI Using Leibniz's formula

The formula is -

X = 4 - 4/3 + 4/5 - 4/7 + 4/9 - ....

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

In this example, the code calculates an approximation of pi using the Leibniz formula for pi, where positive and negative terms alternate. The loop iterates a million times, updating the sum (s) with alternating positive and negative terms.

# 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

Calculating PI Using acos() methods.

In this example, the Python script uses the acos function from the math module to calculate the value of pi (π) up to 3 decimal places. The result is then rounded and printed.

# 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()

3.142

Access Pi (π) Using Math.radians

In this example, the Python script uses the math.radians function to convert 180 degrees to radians. The result, which represents the equivalent angle in radians, is then printed using the print function.

import math
print(math.radians(180))

3.141592653589793

Example: Calculating Area of a Circle Using math.pi

In this example, the Python script defines a function calculate_circle_area that computes the area of a circle given its radius. The script then demonstrates the function by calculating and printing the area for a circle with a radius of 5.0.

import math

def calculate_circle_area(radius):
    area = math.pi * radius**2
    return area

# Example usage:
radius = 5.0
area = calculate_circle_area(radius)
print(f"The area of a circle with radius {radius} is: {area}")

The area of a circle with radius 5.0 is: 78.53981633974483