Python Math Module

Sometimes when working on some kind of financial or scientific project it becomes necessary to implement mathematical calculations in the project. Python provides the math module to deal with such calculations. The math module provides the Python math functions to deal with basic operations such as addition(+), subtraction(-), multiplication(*), division(/) and advanced operations like trigonometric, logarithmic, and exponential functions.

In this article, we learn about the math module from basics to advanced using the help of a huge dataset containing functions explained with the help of good examples.

Math Module in Python

The Python math module provides various values of various constants like pi, and tau. Having such constants saves the time of writing the value of each constant every time we want to use it and that too with great precision. The constants provided by the math module are – 

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

Let’s see each constant in detail.

Euler’s Number in Python 

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

Syntax:

math.e

Example: This code imports the math module and then prints the value of the mathematical constant e.

Python3

import math
print (math.e)

Output:

2.718281828459045

Pi in Python

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 of Python math PI

math.pi

Example 1: This code imports the math module and then prints the value of the mathematical constant pi.

Python3

import math
print (math.pi)

Output:

3.141592653589793

Example 2: Let’s find the area of the circle 

The code utilizes the math module in Python, defines a radius and the mathematical constant pi, and calculates the area of a circle using the formula‘ A = pi * r * r'. It demonstrates the application of mathematical concepts and the usage of the math module for numerical calculations

Python3

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

Output:

50.26548245743669

Python math.tau Constant

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 code imports the math module and then prints the value of the mathematical constant ‘tau'.

Python3

import math
print (math.tau)

Output:

6.283185307179586

Infinite number in Python

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 code imports the math module and then prints the values of positive and negative infinity.

Python3

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

Output:

inf
-inf

Example 2: Comparing the values of infinity with the maximum floating point value

This code imports the math module and then compares the values of positive and negative infinity to the values of 10e108 and -10e108, respectively.

Python3

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

Output:

True
True

NaN Values in Python

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 code imports the math module and then prints the value of math.nan. math.nan represents Not a Number, which is a special value that is used to indicate that a mathematical operation is undefined or the result is not a number.

Python3

import math
print (math.nan)

Output:

nan

Numeric Functions

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.

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 code imports the math module, assigns the value 2.3 to the variable a, and then calculates and prints the ceiling and floor of a.

Python3

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))

Output:

The ceil of 2.3 is : 3
The floor of 2.3 is : 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 code imports the math module, assigns the value 5 to the variable a, and then calculates and prints the factorial of a.

Python3

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

Output:

The factorial of 5 is : 120

Finding the GCD

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

Example: This code imports the math module, assigns the values 15 and 5 to the variables a and b, respectively, and then calculates and prints the greatest common divisor (GCD) of a and b.

Python3

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

Output:

The gcd of 5 and 15 is : 5

Finding the absolute value

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

Example: This code imports the math module, assigns the value -10 to the variable a, and then calculates and prints the absolute value of a.

Python3

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

Output:

The absolute value of -10 is : 10.0

Refer to the below article to get detailed information about the numeric functions.

• 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.

Finding the power of exp

exp() method is used to calculate the power of e i.e.  or we can say exponential of y.

Example: This code imports the math module and then calculates and prints the exponential values of three different input values: an integer, a negative integer, and a float.

Python3

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))

Output:

54.598150033144236
0.049787068367863944
1.0

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 code first prints the string “The value of 3**4 is : ” to the console. Then, it calculates the value of 3 raised to the power of 4 using the pow() function and prints the result to the console.

Python3

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

Output:

The value of 3**4 is : 81.0

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.

This code imports the math module and then calculates and prints the logarithms of three different numbers. The math module provides several functions for working with logarithms, including log(), log2(), and log10().

Python3

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))

Output:

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

Finding the Square root

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

Example: This code imports the math module and then calculates and prints the square roots of three different numbers: 0, 4, and 3.5. The math module provides several functions for working with mathematical operations, including the square root function sqrt().

Python3

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

Output:

0.0
2.0
1.8708286933869707

Refer to the below article to get detailed information about the Logarithmic and Power Functions

• 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.

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 code first imports the math module, which provides a variety of mathematical functions. Then, it defines a variable a and assigns it the value of pi/6, where pi is the mathematical constant representing the ratio of a circle’s circumference to its diameter.

Python3

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))

Output:

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

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 code imports the math module, which provides mathematical functions and constants. It then defines two variables: a and b. a is assigned the value of math.pi/6, which is approximately 0.5235987755982988 radians. b is assigned the value 30, which is 30 degrees.

Python3

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))

Output:

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

Refer to the below articles to get detailed information about the trigonometric and angular functions.

• 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.

Finding gamma value

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

Example: This code imports the math module, which provides mathematical functions and constants. It then defines a variable gamma_var and assigns it the value 6. Next, the code calculates and prints the gamma value of gamma_var using the math module’s gamma() function. The math.gamma() function calculates the gamma value of a given argument.

Python3

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

Output:

The gamma value of the given argument is : 120.0

Check if the value is infinity or NaN

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

Example: This code imports the math module and then checks whether the values of math.pi, math.e, and float('inf') are infinite using the math.isinf() function. The math.isinf() function takes a single argument, which is the value to be checked for infinity. It returns True if the value is infinite and False

Python3

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

Output:

False
False
True

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

Example: This code imports the math module and then checks whether the values of math.pi, math.e, and float('nan') are Not a Number (NaN) using the math.isnan() function. The math.isnan() function takes a single argument, which is the value to be checked for NaN. It returns True if the value is NaN and False.

Python3

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

Output:

False
False
True

Refer to the below article to get detailed information about the special functions.

• Mathematical Functions in Python | Set 4 (Special Functions and Constants)

List of Mathematical function in Python

Function Name	Description
ceil(x)	Returns the smallest integral value greater than the number
copysign(x, y)	Returns the number with the value of ‘x’ but with the sign of ‘y’
fabs(x)	Returns the absolute value of the number
factorial(x)	Returns the factorial of the number
floor(x)	Returns the greatest integral value smaller than the number
gcd(x, y)	Compute the greatest common divisor of 2 numbers
fmod(x, y)	Returns the remainder when x is divided by y
frexp(x)	Returns the mantissa and exponent of x as the pair (m, e)
fsum(iterable)	Returns the precise floating-point value of sum of elements in an iterable
isfinite(x)	Check whether the value is neither infinity not Nan
isinf(x)	Check whether the value is infinity or not
isnan(x)	Returns true if the number is “nan” else returns false
ldexp(x, i)	Returns x * (2**i)
modf(x)	Returns the fractional and integer parts of x
trunc(x)	Returns the truncated integer value of x
exp(x)	Returns the value of e raised to the power x(e**x)
expm1(x)	Returns the value of e raised to the power a (x-1)
log(x[, b])	Returns the logarithmic value of a with base b
log1p(x)	Returns the natural logarithmic value of 1+x
log2(x)	Computes value of log a with base 2
log10(x)	Computes value of log a with base 10
pow(x, y)	Compute value of x raised to the power y (x**y)
sqrt(x)	Returns the square root of the number
acos(x)	Returns the arc cosine of value passed as argument
asin(x)	Returns the arc sine of value passed as argument
atan(x)	Returns the arc tangent of value passed as argument
atan2(y, x)	Returns atan(y / x)
cos(x)	Returns the cosine of value passed as argument
hypot(x, y)	Returns the hypotenuse of the values passed in arguments
sin(x)	Returns the sine of value passed as argument
tan(x)	Returns the tangent of the value passed as argument
degrees(x)	Convert argument value from radians to degrees
radians(x)	Convert argument value from degrees to radians
acosh(x)	Returns the inverse hyperbolic cosine of value passed as argument
asinh(x)	Returns the inverse hyperbolic sine of value passed as argument
atanh(x)	Returns the inverse hyperbolic tangent of value passed as argument
cosh(x)	Returns the hyperbolic cosine of value passed as argument
sinh(x)	Returns the hyperbolic sine of value passed as argument
tanh(x)	Returns the hyperbolic tangent of value passed as argument
erf(x)	Returns the error function at x
erfc(x)	Returns the complementary error function at x
gamma(x)	Return the gamma function of the argument
lgamma(x)	Return the natural log of the absolute value of the gamma function