# Math Module in Python

In this article, you are going to learn everything in detail about the “ math “ module in Python.

We can normally work with general operations using python without importing or implementing any modules into the Python application at that particular instant. But, in some special situations, we may deal with some special and typical cases where we must use the actual and accurate mathematical values and substitute those within the program.

In such situations, we need to import the " math " module. Such types of projects include Financial projects where every value must be accurate enough so that there will be no variation between the expected output and the calculated output. The module " math " is built in order to deal with such types of calculations. The basic operations such as " addition ", " subtraction ", " multiplication ", and " division ", and the complex operations like “ trigonometry “, " logarithms ", etc. can be performed using the Math module in Python.

In this module, we use various constants and methods where those constants possess some fixated values to which they will always be bounded to, and methods lead to the way where the constants can be addressed. The different types of constants that are provided by the " Math " module are listed below.

- Pi ( generally noted as 3.14 and 22/7 )
- Euler’s number ( e )
- Infinity ( can be negative or positive )
- Tau
- Not a Number ( NaN )

Let us learn the syntax and usage of each constant clearly.

### 1. Pi :

**Syntax of Pi:**

math.pi

This statement mentioned in the above syntax allows the user to access the accurate value of the mathematical constant “ pi “. After that, the value of pi can be printed.

**Program to print the value of pi:**

```
# import math module to python application
import math
# assign the value to another variable
a = math.pi
# print the value of pi using the assigned variable " a "
print("The accurate value of the mathematical constant pi is:")
print(a)
```

**The output of the Program:**

```
The accurate value of the mathematical constant pi is:
3.141592653589793
```

**Using the value of “ pi “ in order to find the circumference of the circle:**

```
# program to find the circumference of the circle
# import math module to python application
import math
# assign a value to the radius of the circle
r = 4
# assign the value to another variable
a = math.pi
# print the value of pi using the assigned variable " a "
print("The circumference of the circle with radius 4 is: ")
print(a*r*2)
```

**The output of the Program:**

```
The circumference of the circle with radius 4 is:
25.132741228718345
```

### 2. Euler’s Number:

**Syntax of Euler’s Number:**

math.e

This statement mentioned in the above syntax allows the user to access the accurate value of the mathematical constant “ e “. After that, the value of e can be printed.

**Program to print the value of pi:**

```
# import math module to python application
import math
# assign the value to another variable
a = math.e
# print the value of Euler using the assigned variable " a "
print("The accurate value of the mathematical constant e is:")
print(a)
```

**The output of the Program:**

```
The accurate value of the mathematical constant e is:
2.718281828459045
```

### 3. Infinity

**The syntax for using Infinity with the " math " module:**

math.inf

This statement mentioned in the above syntax allows the user to access the accurate value of the mathematical constant “ inf “. After that, the value of inf can be printed.

In order to have the negative value of infinity, you can introduce the " minus " symbol, i.e., " – " just before the declaration, as shown below.

**Program to print the value of positive infinity and negative infinity:**

```
# import math module to python application
import math
# assign the value to another variable
a = math.inf
b = - math.inf
# print the value of inf and - inf using the assigned variables " a " and " b "
print(a)
print(b
```

**The output of the Program:**

```
-inf
inf
```

Let's check the value of infinity and negative infinity by comparing them with some random numbers.

```
# import math module to python application
import math
# assign the value to another variable
a = math.inf
b = - math.inf
c = - 20
d = 16
# comparing the values of inf and - inf using the assigned variables " a " and " b " with the values of c and d.
print(a<c)
print(b>d)
```

**The output of the Program:**

```
False
False
```

Since the statement is incorrect, the Boolean value " False " is printed, indicating that the print statements are wrong.

### 4. Tau:

The ratio of the circumference to the radius of the circle is defined as the constant “ Tau “. So, the value of “ Tau ” will be the product of 2 and pi.

**Syntax of Tau:**

math.tau

This statement mentioned in the above syntax allows the user to access the accurate value of the mathematical constant “ tau “. After that, the value of tau can be printed.

**Program to print the value of tau:**

```
# import math module to python application
import math
# assign the value to another variable
a = math.tau
# print the value of pi using the assigned variable " a "
print("The accurate value of the mathematical constant tau is:")
print(a)
```

**The output of the Program:**

```
The accurate value of the mathematical constant tau is:
6.283185307179586
```

### 5. Not a Number ( NaN ):

**Syntax of Tau:**

math.nan

**Program to print nan:**

```
# import math module to python application
import math
# assign the value to another variable
a = math.nan
# print nan
print(a)
```

**The output of the Program:**

nan

The different types of functions that can be implemented using the " math " module are listed below.

- ceil()
- floor()
- factorial()
- gcd()
- fabs()
- exp()
- pow()
- log()
- sqrt()
- sin()
- cos()
- tan()
- degrees()
- radians()
- hypot()
- gamma()
- isinf()
- isnan()

Let us learn the syntax and usage of each function clearly.

### 1. ceil()

**Syntax of ceil() function:**

math.ceil()

The role of the ceil() function is to round off the given decimal number to its consecutive integer, which is greater than the integral value of the current number.

Ex: 2.4 is will be rounded into 3 as 3 is the next greater integer of 2 ( which is the integral value of 2.4 ).

**Example program that determines ceil() function:**

```
# import math module to python application
import math
# assign the value to another variable
a = 2.4
b = math.ceil(a)
# print the value before and after using ceil() function to know the difference
print("The value of the given number is: ")
print(a)
print("The value of the number after using ceil() function: ")
print(b)
```

**The output of the Program:**

```
The value of the given number is:
2.4
The value of the number after using ceil() function:
3
```

### 2. floor()

**Syntax of floor() function:**

math.floor()

The role of the floor() function is to round off the given decimal number to its integral value.

Ex: 2.4 is will be rounded into 2 ( as 2 is the integral number of 2.4 ).

**Example program that determines floor() function:**

```
# import math module to python application
import math
# assign the value to another variable
a = 2.4
b = math.floor(a)
# print the value before and after using the floor() function to know the difference
print("The value of the given number is: ")
print(a)
print("The value of the number after using floor() function: ")
print(b)
```

**The output of the Program:**

```
The value of the given number is:
2.4
The value of the number after using the floor() function:
2
```

### 3. factorial()

**Syntax of factorial() function:**

math.factorial()

The role of the function is to determine the factorial of the given integer.

**Example program that determines factorial() function:**

```
# import math module to python application
import math
# assign the value to another variable
a = 4
b = math.factorial(a)
# print the factorial of the number using the factorial() method
print("The factorial of 4 is ", b)
print(b)
```

**The output of the Program:**

The factorial of 4 is: 24

### 4. gcd()

**Syntax of gcd() function:**

math.gcd()

The role of the function gcd() is to determine the Greatest common divisor out of the given integers that can be passed as arguments.

**Example program that determines gcd() function:**

```
# import math module to python application
import math
# assign the values to another variable
a = 4
b = 8
c = math.gcd(a,b)
# print the gcd out of the given 2 numbers using the gcd() method
print("The greatest common divisor out of the numbers 4 and 8 is ", c)
```

**The output of the Program:**

The greatest common divisor out of the numbers 4 and 8 is 4

### 5. fabs()

**Syntax of fabs() function:**

math.fabs()

The role of the function fabs() is to determine the absolute value of the given number.

Ex: When the function fabs() is applied to the number -25 and allowed to print, then the output will be 25.0

**Example program that determines fabs() function:**

```
# import math module to python application
import math
# assign the values to another variable
a = -40
b = math.fabs(a)
# print the absolute value of the number using the fabs() method
print("The absolute value of the number -40 is ", b)
```

**The output of the Program:**

The absolute value of the number -40 is 40.0

### 6. exp()

**Syntax of exp() function:**

math.exp()

The role of the function exp() is to determine and calculate the power of e ( logarithmic e ).

Ex: When the function exp() is applied to the number 4 and allowed to print, then the output will be the result of the calculation of e to the power of 4.

**Example program that determines exp() function:**

```
# import math module to python application
import math
# assign the values to another variable
a = 7
b = math.exp(a)
c = -7
d = math.exp(c)
# print the power of exponential e using the exp() method
print("The result of e to the power 7 is ", b)
print("The result of e to the power -7 is ", d)
```

**The output of the Program:**

```
The result of e to the power 7 is 1096.6331584284585
The result of e to the power -7 is 0.0009118819655545162
```

### 7. pow()

**Syntax of pow() function:**

math.pow()

The role of the function pow() is to determine and calculate the power, i.e., a**b, where b is the power and a is the number.

Ex: When the function pow() is applied to the numbers 4,5 and allowed to print, then the output will be the result of the calculation of 4 to the power of 5.

**Example program that determines exp() function:**

```
# import math module to python application
import math
# assign the values to another variable
a = 4
b = 5
c = math.pow(a,b)
# print the power result using the pow() method
print("The result of 4 to the power 5 is ", c)
```

**The output of the Program:**

The result of 4 to the power 5 is 1024.0

Note: The result of the pow() function will be float always because it converts the data type of the given input into float data type before calculation and execution itself.

### 8. log()

** ****Syntax of log() function:**

math.log()

The role of the log() function is to return logarithmic values of a with b as the base. If the base of the log() function is not given, the value is pre-determined to be of the natural log.

**log2(a)**

**Syntax of log2(a) function:**

math.log2(a)

The role of the log2(a) function is to return the logarithmic value of a with 2 as its base. The value produced as output using this function is more precise than the one mentioned above.

**Log10(a)**

**Syntax of log10(a) function:**

math.log10(a)

The role of this function in the math module is to compute and find the logarithmic value of a with its base as 10. The value produced as output using this function is more precise than the one that is produced using the log() function.

**Example program that determines log(), log2(a), log10(a) functions:**

```
# This code in python is to show the roles of logarithmic functions.
# importing "math" into the program for mathematical operations.
import math
# returning the logarithmic value of 2,3
print ("The value of log 2 with its base as 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))
```

**The output of the Program:**

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

### 9. sqrt()

**Syntax of sqrt() function:**

math.sqrt()

The role of the sqrt() function in python is to produce the square root of a given number as output, i.e., if " a " is a number, then using the sqrt() function, we can find the square root of the number " a ".

Ex: when a number " 16 " is given as input, then using the sqrt() function, we can determine its square root. The output will be " 4 " for the given command.

**Example program that determines sqrt() function:**

```
# this is a python program to show the usage of the sqrt() function.
# importing the math module into the program
import math
# let us print the square root of 1
print(math.sqrt(1))
# let us print the square root of 64
print(math.sqrt(64))
# let us print the square root of 6.25
print(math.sqrt(6.25))
```

**The output of the Program:**

```
1.0
8.0
2.5
```

Here, we can observe that we got the output as intended. Using the sqrt() function, we printed the square roots of 1, 64, and 6.25 numbers. So, this is the usage of the sqrt() function of the math module in python.

### 10. Sin()

**Syntax of sin() function:**

math.sin()

The role of this sin() function is to reduce the burden of calculating the trigonometric values of sine. The math module provides this sin() function as one of its built-in features to return sine values of any angle. The sin() function will only return the sine of the value passed as the argument. The value that is passed in the sin() function must be in radians.

** Example program that determines sin() function:**

```
# This is a code in python to show the usage of the sin() function belonging to the math module.
# First, we have to import "math" for computing the mathematical operations in python.
import math
a = math.pi/3
print ("The trigonometric value of sine of pi/3 is : ", end="")
print (math.sin(a))
# above two lines are written to return the value of sine of pi/3.
```

**The output of the Program:**

The trigonometric value of sine of pi/3 is: 0.8660254037844386

Here, we can observe that the trigonometric value of sine pi/3 is produced as output using the sin() function of the math module. This reduces the complexity of calculation and time consumption for the user.

### 11. Cos()

**Syntax of cos() function:**

math.cos()

The role of the cos() function of the math module in python is to return trigonometric values of a cosine. The value that is passed into this cos() function must be in radians. This function reduces the burden of calculating the trigonometric values of a cosine. The cos() function will only return the cosine of the value passed as the argument.

**Example program that determines cos() function:**

```
# This is a code in python to show the usage of the cos() function belonging to the math module.
# First, we have to import "math" for computing the mathematical operations in python.
import math
a = math.pi/3
print ("The trigonometric value of cosine of pi/3 is : ", end="")
print (math.cos(a))
# above two lines are written to return the value of the cosine of pi/3.
```

**The output of the Program:**

The trigonometric value of the cosine of pi/3 is: 0.5000000000000001

Here, we can observe that the trigonometric value of cosine pi/3 is produced as output using the cos() function of the math module. This reduces the complexity of calculation and time consumption for the user.

### 12. tan()

**Syntax of tan() function:**

math.tan()

The role of this tan() function is to reduce the burden of calculating the trigonometric values of the tangent. The math module provides this tan() function as one of its built-in features to return tangent values of any angle. The tan() function will only return the tangent of the value passed as the argument. The value that is passed in the tan() function must be in radians.

**Example program that determines tan() function:**

```
# This is a code in python to show the usage of the tan() function belonging to the math module.
# First, we have to import "math" for computing the mathematical operations in python.
import math
a = math.pi/3
print ("The trigonometric value of tangent of pi/3 is : ", end="")
print (math.tan(a))
# above two lines are written to return the value of the tangent of pi/3.
```

**The output of the Program:**

The trigonometric value of the tangent of pi/3 is: 1.7320508075688767

Here, we can observe that the trigonometric value of tangent pi/3 is produced as output using the tan() function of the math module. This reduces the complexity of calculation and time consumption for the user.

### 13. degrees()

**Syntax of degrees() function:**

math.degrees()

The role of this degrees() function is to reduce the burden of converting the argument values from radians to degrees. The math module provides this degrees() function as one of its built-in features to return degrees values of any radian value. The degrees() function will only return the degree of the radian value passed as an argument. The value that is passed in the degrees() function must be in radians.

**Example program that determines degrees() function:**

```
# this is a code in python to show the usage of the degrees() function
# belonging to the math module to convert any radians value to degrees.
# we have to import "math" for using mathematical operations in the program.
import math
x = math.pi/3
y = 30
# returning the converted value from radians to degrees
print ("This is the value converted from radians to degrees: ", end="")
print (math.degrees(x))
```

**The output of the Program:**

This is the value converted from radians to degrees: 59.99999999999999

Here, we can observe that the argument value of degrees is produced as output using the degrees() function of the math module. This reduces the complexity of calculation and time consumption for the user.

### 14. radians()

**Syntax of radians() function:**

math.radians()

The role of this radians() function is to reduce the burden of converting the argument values from degrees to radians. The math module provides this radians() function as one of its built-in features to return radian values of any degree value. The radians() function will only return the radian of the degree value passed as an argument. The value that is passed in the radians() function must be in degrees.

**Example program that determines radians() function:**

```
# this is a code in python to show the usage of the " radians() " function
# belonging to the math module to convert any degree's value to radians.
# we have to import "math" for using mathematical operations in the program.
import math
x = math.pi/3
y = 30
# returning the converted value from degrees to radians
print ("This is the value converted from degrees to radians: ", end="")
print (math.radians(x))
```

**The output of the Program:**

This is the value converted from degrees to radians: 0.018277045187202513

Here, we can observe that the argument value of degrees is produced as output using the degrees() function of the math module. This reduces the complexity of calculation and time consumption for the user.

### 15. hypot()

**Syntax of hypot() function:**

math.hypot()

The role of this hypot() function is to reduce the burden of calculating the trigonometric value of the hypotenuse. The math module provides this hypot() function as one of its built-in features to return the hypotenuse value of any triangle. The hypot() function will only return the hypotenuse of the value passed as the argument.

**Example program that determines hypot() function:**

```
# this is a code in python to show the usage of the hypot() function belonging to the math module
# importing "math" for mathematical operations
import math
from tkinter import X, Y
X = 4
Y = 3
# to return the hypotenuse value of 3 and 4
print ("The value of hypotenuse of 3 and 4 is : ", end="")
print (math.hypot(X,Y))
```

**The output of the Program:**

The value of hypotenuse of 3 and 4 is: 5.0

Here, we can observe that the argument value of the hypotenuse is produced as output using the hypot() function of the math module. This reduces the complexity of calculation and time consumption for the user.

### 16. gamma()

**Syntax of gamma() function:**

math.gamma( gamma_var )

The gamma function is not a numeric function or a logarithmic function. The gamma function belongs to the category of **special functions.** These special functions do not come under any category that we saw above. The special functions are used at different points of coding using the math module in python. The gamma function “ gamma() ” can be used to return the gamma value of a given argument.

**Example program that determines gamma() function:**

```
# This is a code in python to show the usage of the hypot() function belonging to the math module
# importing "math" for mathematical operations
import math
# initialize the gamma argument in the below line.
gamma_var = 15
# Printing the gamma value below.
print ("The gamma value of the argument passed above is : " + str(math.gamma(gamma_var)))
```

**The output of the Program:**

The gamma value of the given argument is: 87178291200.0

Here, we can observe that the argument is initialized with a value of 15. The argument is passed using the gamma() function in the next command. So, the output returned the gamma value of 15, i.e., " 87178291200.0 ”.

### 17. isinf()

**Syntax of isinf() function:**

math.isinf( any_variable )

The isinf() function is not a numeric function or a logarithmic function. The isinf() function belongs to the category of **special functions.** These special functions do not come under any category that we saw above. The special functions are used at different points of coding using the math module in python. The infinity function “ isinf() ” can be used to check whether a given variable’s value is infinity or not. A statement containing the isinf() function returns a Boolean value as its output.

**Example program that determines isinf() function:**

```
# This is a code in python to show the usage of the isinf() function belonging to the math module
# importing "math" for mathematical operations
import math
# checking the isinf() function with different inbuilt numbers.
print (math.isinf(math.e))
print (math.isinf(math.pi))
# checking the same for a inf value
print (math.isinf(float('inf')))
```

**The output of the Program:**

```
False
False
True
```

Here, we can observe that the argument is initialized with different in-built numbers. The argument is passed using the isinf() function in the next command. So, the output returned Boolean values, i.e., either true or false.

### 18. isnan()

**Syntax of isnan() function:**

math.isnan( any_variable )

The isnan() function is not a numeric function or a logarithmic function. The isnan() function belongs to the category of **special functions.** These special functions do not come under any category that we saw above. The special functions are used at different points of coding using the math module in python. The “ is not a number ” function isnan() can be used to check whether a given variable’s value is a number or not. A statement containing the isnan() function returns a Boolean value as its output.

**Example program that determines isnan() function:**

```
# This is a code in python to show the usage of the isnan() function belonging to the math module
# importing "math" for mathematical operations
import math
# checking the isnan() function with different inbuilt numbers.
print (math.isnan(math.e))
print (math.isnan(math.pi))
# checking the same for a NaN value
print (math.isnan(float('nan')))
```

**The output of the Program:**

```
False
False
True
```

Here, we can observe that the argument is initialized with different in-built numbers. The argument is passed using the isnan() function in the next command. So, the output returned Boolean values, i.e., either true or false.

## Conclusion:

In this article, we have learnt about the usage and working of the math module in python. We have also learnt which functions are in-built into the math module and how they are used.