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Python Math Module

  • Last Updated : 18 Aug, 2021

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

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

Constants provided by the math module

Math module provides various the value of various constants like pi, 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. 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 

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



Syntax:

math.e

Example:

Python3




# Import math Library
import math
 
# Print the value of Euler e
print (math.e)

Output:

2.718281828459045

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:



Python3




# Import math Library
import math
 
# Print the value of pi
print (math.pi)

Output:

3.141592653589793

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

Python3




# Import math Library
import math
 
# radius of the circle
r = 4
 
# value of pie
pie = math.pi
 
# area of the circle
print(pie * r * r)

Output:

50.26548245743669

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:

Python3




# Import math Library
import math
 
# Print the value of tau
print (math.tau)

Output:

6.283185307179586

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 math.inf constant returns of positive infinity. For negative infinity, use -math.inf.

Syntax:



math.inf

Example 1:

Python3




# Import math Library
import math
 
# Print the positive infinity
print (math.inf)
 
# Print the negative infinity
print (-math.inf)

Output:

inf
-inf

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

Python3




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

Output:

True
True

NaN

The 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:

Python3




# Import math Library
import math
 
# Print the value of nan
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:

Python3




# Python code to demonstrate the working of
# ceil() and floor()
 
# importing "math" for mathematical operations
import math
 
a = 2.3
 
# returning the ceil of 2.3
print ("The ceil of 2.3 is : ", end="")
print (math.ceil(a))
 
# returning the floor of 2.3
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:

Python3




# Python code to demonstrate the working of
# factorial()
 
# importing "math" for mathematical operations
import math
 
a = 5
 
# returning the factorial of 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:

Python3




# Python code to demonstrate the working of
# gcd()
 
# importing "math" for mathematical operations
import math
 
a = 15
b = 5
 
# returning the gcd of 15 and 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:



Python3




# Python code to demonstrate the working of
# fabs()
 
# importing "math" for mathematical operations
import math
 
a = -10
 
# returning the absolute value.
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.

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. e^y         or we can say exponential of y.

Example:

Python3




# Python3 code to demonstrate
# the working of exp()
import math
 
# initializing the value
test_int = 4
test_neg_int = -3
test_float = 0.00
 
# checking exp() values
# with different numbers
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:

Python3




# Python code to demonstrate pow()
# version 1
 
print ("The value of 3**4 is : ",end="")
 
# Returns 81
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.

Python3




# Python code to demonstrate the working of
# logarithm
 
# importing "math" for mathematical operations
import math
 
 
# returning the log of 2,3
print ("The value of log 2 with base 3 is : ", end="")
print (math.log(2,3))
 
# returning the log2 of 16
print ("The value of log2 of 16 is : ", end="")
print (math.log2(16))
    
# returning the log10 of 10000
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:

Python3




# Python3 program to demonstrate the
# sqrt() method
 
# import the math module
import math
 
# print the square root of 0
print(math.sqrt(0))
 
# print the square root of 4
print(math.sqrt(4))
 
# print the square root of 3.5
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

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:

Python3




# Python code to demonstrate the working of
# sin(), cos(), and tan()
 
# importing "math" for mathematical operations
import math
 
a = math.pi/6
 
# returning the value of sine of pi/6
print ("The value of sine of pi/6 is : ", end="")
print (math.sin(a))
 
# returning the value of cosine of pi/6
print ("The value of cosine of pi/6 is : ", end="")
print (math.cos(a))
 
# returning the value of tangent of pi/6
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:

Python3




# Python code to demonstrate the working of
# degrees() and radians()
 
# importing "math" for mathematical operations
import math
 
a = math.pi/6
b = 30
 
# returning the converted value from radians to degrees
print ("The converted value from radians to degrees is : ", end="")
print (math.degrees(a))
 
# returning the converted value from degrees to radians
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.

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:

Python3




# Python code to demonstrate
# working of gamma()
import math
 
# initializing argument
gamma_var = 6
 
# Printing the gamma value.
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:

Python3




# Python3 code to demonstrate
# the working of isnan()
import math
 
# checking isnan() values
# with inbuilt numbers
print (math.isinf(math.pi))
print (math.isinf(math.e))
 
 
# checking for NaN value
print (math.isinf(float('inf')))

Output:

False
False
True

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

Example:

Python3




# Python3 code to demonstrate
# the working of isnan()
import math
 
# checking isnan() values
# with inbuilt numbers
print (math.isnan(math.pi))
print (math.isnan(math.e))
 
 
# checking for NaN value
print (math.isnan(float('nan')))

Output:

False
False
True

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

List of Mathematical function in Python

Function NameDescription
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 

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