The math module in Python is a built-in library that contains a collection of mathematical functions and constants. It is commonly used to perform standard math operations such as rounding, trigonometry, logarithms and more, all with precise and reliable results.

Why do we need Math module ?

1. Provides built-in functions for complex math operations like square root, power and trigonometry.
2. Offers constants like pi and e, useful in scientific and engineering calculations.
3. Improves accuracy and performance over manual calculations or custom functions.
4. Helps in performing logarithmic and exponential operations easily.
5. Supports real-world applications like physics, statistics, geometry and finance.

Importing math module

To work with mathematical constants and functions in Python, you need to import the math module:

import math

Once imported, you can access a variety of constants. Let’s explore some of them:

Constants in Math Module

The Python math module provides various values of various constants like pi and tau. We can easily write their values with these constants. The constants provided by the math module are:

• Euler's Number
• Pi
• Tau
• Infinity
• Not a Number (NaN)

Let's see constants in math module with examples:

1. Euler's Number

The math.e constant returns the Euler’s number: 2.71828182846.

Syntax:

math.e

Example: This prints the value of the mathematical constant e.

import math 
print (math.e)

2.718281828459045

2. Pi

You all must be familiar with pi. The pi is depicted as either 22/7 or 3.14. math.pi provides a more precise value for the pi.

Syntax:

math.pi

Example 1: This prints the value of the mathematical constant pi.

import math  
print (math.pi)

3.141592653589793

Example 2: This calculates the area of a circle using pi

import math 
r = 4
pie = math.pi
print(pie * r * r)

50.26548245743669

3. tau

Tau is defined as the ratio of the circumference to the radius of a circle. The math.tau constant returns the value tau: 6.283185307179586.

Syntax:

math.tau

Example: This prints the value of the mathematical constant tau.

import math 
print (math.tau) 

6.283185307179586

4. Infinity

Infinity basically means something which is never-ending or boundless from both directions i.e. negative and positive. It cannot be depicted by a number. The Python math.inf constant returns of positive infinity. For negative infinity use -math.inf.

Syntax:

math.inf

Example 1: This prints positive and negative infinity.

import math 
print (math.inf) 
print (-math.inf) 

inf
-inf

Example 2: This compares infinity with a large number.

import math 
print (math.inf > 10e108) 
print (-math.inf < -10e108) 

True
True

5. NaN Values

The Python math.nan constant returns a floating-point nan (Not a Number) value. This value is not a legal number. The nan constant is equivalent to float(“nan”).

Example: This prints the value of math.nan.

import math 
print (math.nan) 

nan

Numeric Functions in Math Module

In this section, we will deal with the functions that are used with number theory as well as representation theory such as finding the factorial of a number. We will discuss these numerical functions along with examples and use-cases.

1. Finding the ceiling and the floor value

Ceil value means the smallest integral value greater than the number and the floor value means the greatest integral value smaller than the number. This can be easily calculated using the ceil() and floor() method respectively.

Example: This prints the ceiling and floor value of 2.3.

import math 
a = 2.3
print ("The ceil of 2.3 is : ", end="") 
print (math.ceil(a)) 
print ("The floor of 2.3 is : ", end="") 
print (math.floor(a)) 

The ceil of 2.3 is : 3
The floor of 2.3 is : 2

2. Finding the factorial of the number

Using the factorial() function we can find the factorial of a number in a single line of the code. An error message is displayed if number is not integral.

Example: This prints the factorial of 5.

import math
a = 5
print("The factorial of 5 is : ", end="")
print(math.factorial(a))

The factorial of 5 is : 120

3. Finding the GCD

gcd() function is used to find the greatest common divisor of two numbers passed as the arguments. 

Example: This prints the GCD of 15 and 5.

import math 
a = 15
b = 5
print ("The gcd of 5 and 15 is : ", end="") 
print (math.gcd(b, a)) 

The gcd of 5 and 15 is : 5

4. Finding the absolute value

fabs() function returns the absolute value of the number.

Example: This prints the absolute value of -10

import math 
a = -10
print ("The absolute value of -10 is : ", end="") 
print (math.fabs(a))

The absolute value of -10 is : 10.0

To know more, refer Mathematical Functions in Python | Set 1 (Numeric Functions)

Logarithmic and Power Functions

Power functions can be expressed as x^n where n is the power of x whereas logarithmic functions are considered as the inverse of exponential functions.

1. Finding the power of exp

exp() method is used to calculate the power of e i.e. e^y        

Example: This prints exponential values of an integer, negative integer and a float.

import math 
test_int = 4
test_neg_int = -3
test_float = 0.00
print (math.exp(test_int)) 
print (math.exp(test_neg_int)) 
print (math.exp(test_float)) 

54.598150033144236
0.049787068367863944
1.0

2. Finding the power of a number

pow() function computes x**y. This function first converts its arguments into float and then computes the power.

Example: This prints 3 raised to the power of 4.

print ("The value of 3**4 is : ",end="")
print (pow(3,4))

The value of 3**4 is : 81

3. Finding the Logarithm

• log() function returns the logarithmic value of a with base b. If the base is not mentioned, the computed value is of the natural log.
• log2(a) function computes value of log a with base 2. This value is more accurate than the value of the function discussed above.
• log10(a) function computes value of log a with base 10. This value is more accurate than the value of the function discussed above.

Example: This prints different logarithmic values.

import math 
print ("The value of log 2 with base 3 is : ", end="") 
print (math.log(2,3)) 
print ("The value of log2 of 16 is : ", end="") 
print (math.log2(16)) 
print ("The value of log10 of 10000 is : ", end="") 
print (math.log10(10000)) 

The value of log 2 with base 3 is : 0.6309297535714574
The value of log2 of 16 is : 4.0
The value of log10 of 10000 is : 4.0

4. Finding the Square root

sqrt() function returns the square root of the number. 

Example: This prints square roots of 0, 4 and 3.5.

import math 
print(math.sqrt(0)) 
print(math.sqrt(4)) 
print(math.sqrt(3.5)) 

0.0
2.0
1.8708286933869707

To know more, refer Mathematical Functions in Python | Set 2 (Logarithmic and Power Functions)

Trigonometric and Angular Functions

You all must know about Trigonometric and how it may become difficult to find the values of sine and cosine values of any angle. Math module provides built-in functions to find such values and even to change the values between degrees and radians.

1. Finding sine, cosine and tangent

sin(), cos() and tan() functions returns the sine, cosine and tangent of value passed as the argument. The value passed in this function should be in radians.

Example: This prints the trigonometric values of π/6.

import math 
a = math.pi/6
print ("The value of sine of pi/6 is : ", end="") 
print (math.sin(a)) 
print ("The value of cosine of pi/6 is : ", end="") 
print (math.cos(a)) 
print ("The value of tangent of pi/6 is : ", end="") 
print (math.tan(a)) 

The value of sine of pi/6 is : 0.49999999999999994
The value of cosine of pi/6 is : 0.8660254037844387
The value of tangent of pi/6 is : 0.5773502691896257

2. Converting values from degrees to radians and vice versa

• degrees() function is used to convert argument value from radians to degrees.
• radians() function is used to convert argument value from degrees to radians.

Example: This converts π/6 radians to degrees and 30° to radians.

import math 
a = math.pi/6
b = 30
print ("The converted value from radians to degrees is : ", end="") 
print (math.degrees(a)) 
print ("The converted value from degrees to radians is : ", end="") 
print (math.radians(b)) 

The converted value from radians to degrees is : 29.999999999999996
The converted value from degrees to radians is : 0.5235987755982988

To know more, refer Mathematical Functions in Python | Set 3 (Trigonometric and Angular Functions)

Special Functions

Besides all the numeric, logarithmic functions we have discussed yet, the math module provides some more useful functions that does not fall under any category discussed above but may become handy at some point while coding.

1. Finding gamma value

The gamma() function is used to return the gamma value of the argument.

Example: This prints the gamma of 6.

import math 
gamma_var = 6
print ("The gamma value of the given argument is : "
                    + str(math.gamma(gamma_var))) 

The gamma value of the given argument is : 120.0

2. Check if the value is infinity or NaN

isinf() function is used to check whether the value is infinity or not.

Example: Checking for infinity.

import math 
print (math.isinf(math.pi)) 
print (math.isinf(math.e)) 
print (math.isinf(float('inf'))) 

False
False
True

isnan() function returns true if the number is "NaN" else returns false.

Example: Checking for NaN.

import math 
print (math.isnan(math.pi)) 
print (math.isnan(math.e)) 
print (math.isnan(float('nan'))) 

False
False
True

To know more, refer Mathematical Functions in Python | Set 4 (Special Functions and Constants)

List of Mathematical function in Math Module

Here is the list of all mathematical functions in math module, you can use them when you need it in program: