In this tutorial, you will learn about Python math functions in the **math** module of Python. Mathematical calculations are always required in any type of project.

However, the math module does not work on complex numbers and you need to use the cmath module to perform operations on complex numbers.

In Python, some built-in math operators do not require the math module such as addition, subtraction, multiplication, division.

The advanced operations such as trigonometric (sin, cos, etc.), logarithmic, exponential, or factorial, etc. are not built-in. That’s why the math module is imported.

## Math constants

In addition to the advanced mathematical operations, the math module also provides predefined mathematical constants that are:

- Pi (math.pi)
- Euler’s number (math.e)
- Tau (math.tau)
- Infinity (math.inf)
- Not a number (math.nan)

### Pi

Pi is a mathematical constant defined as the ratio of the circumference of a circle to the diameter of the circle.

Π = c/d

Where c is the circumference of the circle and d is the diameter of the circle. The value of pi is 3.14. Pi (Π) can be accessed in Python as:

**Code:**

import math math.pi #3.141592653589793

**Output:**

Consider the following example where we used pi to find the circumference of a circle:

**Code:**

import math radius = 5 circumference = 2 * math.pi * radius print ("Circumference of circle = ", circumference)

**Output:**

### Euler’s Number (e)

Euler’s number is the base of the natural logarithm. It is denoted by symbol e. The value of e is approximated to be 2.718. Euler’s number can be accessed in Python as follows:

**Code:**

import math math.e #2.718281828459045

**Output:**

### Tau

Tau (𝜏) is a mathematical constant, defined as the ratio of the circumference of the circle to the radius of the circle.

math.tau = 2*pi

Check out the code below:

**Code:**

import math math.tau #6.283185307179586

**Output:**

### Infinity

Infinity is a boundless entity that cannot be defined in numbers. In Python, positive and negative infinities are defined as follows:

**Code:**

import math math.inf -math.inf

**Output:**

Infinity is used to compare given numbers to the absolute maximum and absolute minimum values as demonstrated in the code below:

**Code:**

import math x = 13.789 x < math.inf x < -math.inf

**Output:**

### Not a number (nan)

Not a number (nan) refers to non-numerical values. Not a number (nan) makes sure that the value of a given numerical variable is a number.

**Code:**

import math math.nan

**Output:**

## floor() method

The floor() method of the math module **rounds down** a number to the nearest integer. Syntax for floor() is given below:

**Syntax:**

math.floor(x)

- x is the input number. The floor() method takes positive or negative numbers as input.

The floor() method returns the nearest integer less than or equal to x. If the number is a floating-point number, 10.89, floor() will return 10.

If the number is an integer, floor() will return the same integer. Consider the following example:

**Code:**

import math x = 3.5367 math.floor(x) x = 6 math.floor(x)

**Output:**

## ceil() method

The ceil() method of the math module **rounds up** a number to the nearest integer. Syntax for ceil() is given below:

**Syntax:**

math.ceil(x)

- x is the input number. The ceil() method takes positive or negative numbers as input.

The ceil() method returns an integer value greater than or equal to x. If the number is a floating-point number, 10.89, ceil() will return 11.

If the number is an integer, ceil() will return the same integer. The following example explains the ceil() method:

**Code:**

import math x = 10.89 math.ceil(x) x = 10 math.ceil(x)

**Output:**

## math.sqrt()

The sqrt() method returns the square root of an input value. The syntax of sqrt() is as follows:

**Syntax:**

math.sqrt(x)

- x is the input number. It must be greater than or equal to 0. If x is less than 0 (negative number), sqrt() will return
**ValueError**.

The sqrt() method returns a floating-point number. Consider the example below:

**Code:**

import math math.sqrt(9) math.sqrt(4) math.sqrt(24) math.sqrt(-49)

**Output:**

If the number is less than 0, we will have the following error:

## math.fabs(x)

**fabs** represents the absolute function. The absolute function returns a non-negative value of the given number.

It means that the absolute value of a positive number will be the same number and if the given number is negative, the fabs function will convert it into a positive number.

For example, the fabs value of -8 will be 8 and the fabs value of 8 will be 8. Syntax of fabs is given below:

**Syntax:**

math.fabs(x)

- x can be an integer or a floating-point.

The method will return a non-negative floating-point number. Consider the following example:

**Code:**

import math math.fabs(-3) math.fabs(-89.9) math.fabs(89)

**Output:**

The difference between math.fabs() method and the python’s abs() method is that the math.fabs() method always returns a floating-point number.

## math.pow(x)

The pow() method of the math module returns the value of input number x raised to the power y that is **x ^{y}**.

The syntax for math.pow() is as follows:

**Syntax:**

math.pow(x, y)

- x is the input number and y is the power of x. If x is 3 and y equals 4, it will mean: 3
^{4 = 3 * 3 * 3 * 3.}

The function returns a floating-point value.

In mathematics, anything raised to power 0 equals 1, and 1 raised to power anything also equals 1. Therefore, the pow() method will return 1.0 if y is 0 and x is any number.

Similarly, pow() will return 1.0 if x is 1 and y is any number.

math.pow(x, 0.0) = 1.0 math.pow(1.0, y) = 1.0

**Output:**

**Code:**

import math print("3 raised to power 4 = ", math.pow(3, 4))

**Output:**

## math.isclose()

The isclose() method of the math module uses relative and absolute tolerance to check the closeness of two values. Tolerance is defined as the threshold to check the closeness of the numbers.

If the two numbers are close to each other, the isclose() method will return true and return false if they are not close to each other.

The syntax of isclose() is given below:

**Syntax:**

math.isclose(a, b, rel_tol, abs_tol)

- a and b are the numbers to check the closeness of.
- rel_tol (optional) is the relative tolerance and is defined as the maximum difference between the input values (a and b). The default value of rel_tol is: 1e-09 or 0.000000001. rel_tol should be greater than 0.
- abs_tol (optional) is the minimum absolute tolerance. abs_tol compares values nearer to 0. abs_tol should be at least 0.

The math.isclose() method returns Boolean value:

- True if the given numbers are close.
- False if the given numbers are not close.

Check out the code below:

**Code:**

import math print(math.isclose(12.014, 12.56)) print(math.isclose(12.014, 12.014)) print(math.isclose(12.45, 12.46)) print(math.isclose(12.014, 12.434, abs_tol = 0.5)) print(math.isclose(12.014, 12.018, rel_tol = 0.2))

**Output:**

## math.factorial()

The factorial() method of the math module returns the factorial of the given number. The input number must be a positive number.

Factorial of a number is the multiplication of numbers starting from the input number back to 1.

**Syntax:**

math.factorial(x)

- x should be a positive integer. If x is non-integer or negative, you will get a
**ValueError**.

The math.factorial() method returns a positive int value. The following code uses math.factorial():

**Code:**

import math print("factorial of 3 = ", math.factorial(3)) print("factorial of 4 = ", math.factorial(4)) print("factorial of 14 = ", math.factorial(14))

**Output:**

## math.prod()

The prod() method of the math module works on iterables. It returns the product of all elements in an iterable or sequence. The syntax of the math.prod() method is as follows:

**Syntax:**

math.prod(iterable, start)

**iterable**is the input sequence. The elements of the iterable must be numeric.**start**is the starting value of the product. The default value of start is 1.

If the iterable is empty, prod() will return the start value. math.prod() is used in the code below:

**Code:**

import math my_list = [2, 3, 7, 6] print("Product of elements of my list = ", math.prod(my_list))

**Output:**

If the iterable is empty:

**Code:**

my_list = [] print("Product of elements of my list = ", math.prod(my_list))

**Output:**

Note that math.prod() is not defined in the versions older than 3.8.

## math.fsum()

The fsum() method is used to find the sum of the elements of an iterable. The syntax for math.fsum() method is as follows:

**Syntax:**

math.fsum(iterable)

- iterable is the input sequence.

The fsum() method returns an accurate floating-point number after calculating the sum of elements.

**Code:**

import math my_list = [2, 2, 8, 10, 34] print("Sum of elements of my list = ", math.fsum(my_list)) my_list = [1.8, 9, 33.4, 8.64, 3.98] print("Sum of elements of my list = ", math.fsum(my_list))

**Output:**

## math.fmod()

The fmod() method of the math module calculates the modulo of the given numbers. Modulo means, it returns the remainder of x/y.

**Syntax:**

math.fmod(x, y)

- x is the numerator in the fraction x/y
- y is the denominator in the fraction x/y
- x and y can be negative or positive but they must be numbers.
- If x and y, both are 0, you will get an error.
- If y = 0, you will get an error.

The fmod() method returns a floating-point value. Consider the following example:

**Code:**

import math x = 56 y = 3 print("Remainder of ", x, "/", "y =", math.fmod(x, y))

**Output:**

## math.log()

The log() method of the math module calculates the natural logarithm of the input value.

The math.log() method can have 1 or 2 arguments:

- If the method has 1 argument x, the log is calculated as x log to the base e.
- If the method has 2 arguments x and y, the log is calculated as x log to the base y.

The syntax of math.log() is as follows:

**Syntax:**

math.log(x, y)

- x is the number to calculate the natural logarithm of. x must be greater than 0.
- If x is a negative number or 0, you will get ValueError.
- If x is not a number, you will get TypeError.
- y is optional. y is the base. If y is not specified, the default base will be e.

The log() method returns a floating-point value.

**Code:**

import math print("natural logarithm of 2.9845 = ", math.log(2.9845)) print("3.956 log to base 2 = ", math.log(3.956, 2))

**Output:**

## math.log10()

The log10() method calculates the logarithm of the input number to the base 10.

**Syntax:**

math.log10(x)

- x is the input number to find the logarithm of. x should be greater than 0.

The math.log10() method will return a floating-point value after calculating the base-10 logarithm.

**Code:**

import math print("Log of 24.89 to the base 10 = ", math.log(24.89))

**Output:**

## math.exp()

The method math.exp() will return E raised to power x. Here E is the base of the natural logarithm approximately equals 2.718282.

**Syntax:**

math.exp(x)

The method math.exp() will return floating-point value from E^{x}.

**Code:**

import math print("E raised to power 5 = ", math.exp(5)) print("E raised to power 8 = ", math.exp(8))

**Output:**

## math.erf()

The math.erf() method of the math module finds the error function of the input number. The syntax of math.erf() is given below:

**Syntax:**

math.erf(x)

- x is the input number to find the error function. x should be within the range of -infinity to +infinity.

The math.erf() method returns a floating-point value ranging from -1 to +1. Consider the following example:

**Code:**

import math x = 3.6 print("Error function of x = ", math.erf(x))

**Output:**

## math.gcd() (Greatest Common Divisor)

The math.gcd() method of the math module calculates the greatest common divisor of two input numbers of data type int.

**Syntax:**

math.gcd(x, y)

- x and y are the input numbers. Both x and y should be of data type int.
- floating-point numbers are not allowed in the gcd() method.

The math.gcd() method will return an int type value after finding the greatest common divisor of x and y. If both input numbers are 0, math.gcd() will return 0. Empty gcd() also returns 0.

GCD is the greatest common divisor that divides two input numbers and does not return any remainder value. Consider the code example below:

**Code:**

import math x = 44 y = 16 print("Greatest common divisor of ", x, " and ", y, " = ", math.gcd(x, y))

**Output:**

## Angular Conversion Methods

In the Python math module, there are two helper functions to manipulate angles:

- math.degrees()
- math.radians()

### math.degrees

The math.degrees() method is used to convert the given angle from radians to degrees.

**Syntax:**

math.degrees(x)

- x is the given angle that is to be converted from radians to degrees

The method returns a floating-point value that represents the angle in degrees.

**Code:**

import math angle = 45 print("Angle is degrees = ", math.degrees(angle))

**Output:**

### math.radians

The math.radians() method converts the given angle from degrees to radians.

**Syntax:**

math.radians(x)

- x is the given angle that is to be converted from degrees to radians

The method returns a floating-point value that represents the angle in radians.

**Code:**

import math angle = 2578.3100780887044 print("Angle is radians = ", math.radians(angle))

**Output:**

## Trigonometric Methods

The following functions are defined in the math module to perform trigonometric operations:

### math.sin()

The sin() method of the math module returns the sine of the given angle.

**Syntax:**

math.sin(x)

- x is the input angle. x must be a number.

The sin() method returns a floating-point value ranging from -1 to 1. If the input value is given in degrees, it must be converted to radians.

**Code:**

import math angle = 20 angle_radians = math.radians(angle) print("Sine value of 20 degrees = ", math.sin(angle_radians))

**Output:**

Consider the following example in which we will plot the values from sin() method using pyplot:

**Code:**

import math import matplotlib.pyplot as plt x = [-4.8, -2.4, -0.14, 0.14, 2.4, 4.8] y = [] for i in range(len(x)): y.append(math.sin(x[i])) plt.plot(x, y, marker = “x”) plt.show()

**Output:**

### math.cos()

The cos() method of the math module returns the cosine of the given angle.

**Syntax:**

math.cos(x)

- x is the input angle. x must be a number.

The cos() method returns a floating-point value ranging from -1 to 1. If the input value is given in degrees, it must be converted to radians.

**Code:**

import math angle = 20 angle_radians = math.radians(angle) print("Cos of angle 20 = ", math.cos(angle_radians))

**Output:**

Consider the following example in which we will plot the values from the cos() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-4.8, -2.4, -0.14, 0.14, 2.4, 4.8] y = [] for i in range(len(x)): y.append(math.cos(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

### math.tan()

The tan() method of the math module returns the tangent of the given angle.

**Syntax:**

math.tan(x)

- x is the input angle. x must be a number.

The tan() method returns a floating-point value. If the input value is given in degrees, it must be converted to radians.

**Code:**

import math angle = 20 angle_radians = math.radians(angle) print("Tan of angle 20 = ", math.tan(angle_radians))

**Output:**

Consider the following example in which we will plot the values from tan() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-4.8, -2.4, -0.14, 0.14, 2.4, 4.8] y = [] for i in range(len(x)): y.append(math.tan(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

### math.sinh()

The sinh() method of the math module finds the hyperbolic sine of an angle.

**Syntax:**

math.sinh(x)

- x is the input angle. x must be a number.

The sinh() method returns a floating-point value. If the input value is given in degrees, it must be converted to radians.

**Code:**

import math angle = 20 angle_radians = math.radians(angle) print("Hyperbolic sine of angle 20 = ", math.sinh(angle_radians))

**Output:**

Consider the following example in which we will plot the values from sinh() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-5.698, -3.028, -1.318, 1.318, 3.028, 5.698] y = [] for i in range(len(x)): y.append(math.sinh(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

### math.cosh()

The cosh() method of the math module finds the hyperbolic cosine of an angle.

**Syntax:**

math.cosh(x)

- x is the input angle. x must be a number.

The cosh() method returns a floating-point value. If the input value is given in degrees, it must be converted to radians.

**Code:**

import math angle = 30 angle_radians = math.radians(angle) print("Hyperbolic cosine of angle 30 = ", math.cosh(angle_radians))

**Output:**

Consider the following example in which we will plot the values from cosh() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-5.698, -3.028, -1.318, 1.318, 3.028, 5.698] y = [] for i in range(len(x)): y.append(math.cosh(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

### math.asin()

The asin() method of the math module finds the arcsine of an angle in radians.

**Syntax:**

math.asin(x)

- x is the input angle. x must be a number. x should be within the range of -1 to 1.

The asin() method returns a floating-point value.

**Code:**

import math print("arc sine of 0.8 = ", math.asin(0.8))

**Output:**

If x is greater than 1, you will get an error as shown below:

Consider the following example in which we will plot the values from asin() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-1, -0.8, -0.5, 0.5, 0.8, 1] y = [] for i in range(len(x)): y.append(math.asin(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

### math.acos()

The acos() method of the math module finds the arccosine of an angle in radians.

**Syntax:**

math.acos(x)

- x is the input angle. x must be a number. x should be within the range of -1 to 1.

The acos() method returns a floating-point value.

**Code:**

import math print("arc cos of 0.8 = ", math.acos(0.8))

**Output:**

Consider the following example in which we will plot the values from acos() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-1, -0.8, -0.5, 0.5, 0.8, 1] y = [] for i in range(len(x)): y.append(math.acos(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

### math.atan()

The atan() method of the math module finds the arctangent of an angle in radians.

**Syntax:**

math.atan(x)

- x is the input angle. x must be a number.

The atan() method returns a floating-point value ranging from -pi/2 to pi/2.

**Code:**

import math print("arc tan of 0.8 = ", math.atan(0.8))

**Output:**

Consider the following example in which we will plot the values from atan() method on a graph:

**Code:**

import math import matplotlib.pyplot as plt x = [-2, -1.8, -0.5, 0.5, 1.8, 2] y = [] for i in range(len(x)): y.append(math.atan(x[i])) plt.plot(x, y, marker = "x") plt.show()

**Output:**

I hope you find the tutorial useful. Keep coming back.

Mokhtar is the founder of LikeGeeks.com. He works as a Linux system administrator since 2010. He is responsible for maintaining, securing, and troubleshooting Linux servers for multiple clients around the world. He loves writing shell and Python scripts to automate his work.

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