hypot() function - Python

math.hypot() function in Python is used to compute the Euclidean distance from the origin (0, 0) to a point (x, y) in a 2D plane. It calculates the hypotenuse of a right triangle, given the lengths of the two other sides.

Example

import math

x = 3
y = 4

res = math.hypot(x, y)
print(res) 

5.0

Explanation:

In this example, the two sides of the right triangle are 3 and 4. The hypot() function calculates the hypotenuse as:

\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0

Thus, the output is 5.0, which is the length of the hypotenuse.

Syntax of hypot() method

math.hypot(x, y)

Parameters

• x and y are numerical values

Return Type

• Returns a float value having Euclidean norm, \sqrt{(x^2 + y^2)}.

Error

• When more than two arguments are passed, it returns a TypeError.

Note : One has to import math module before using hypot() function.  

Examples of hypot() method

1. Basic Hypotenuse Calculation 

This example demonstrates how the hypot() function works with positive and negative values to compute the hypotenuse.

import math

# Use of hypot function
print("hypot(3, 4) : ", math.hypot(3, 4))

# Neglects the negative sign
print("hypot(-3, 4) : ", math.hypot(-3, 4))

print("hypot(6, 6) : ", math.hypot(6, 6))

hypot(3, 4) :  5.0
hypot(-3, 4) :  5.0
hypot(6, 6) :  8.48528137423857

Explanation

• math.hypot(3, 4) computes \sqrt{(3^2 + 4^2)} = 5.0.
• math.hypot(-3, 4) also returns 5.0 since the negative sign is ignored.
• math.hypot(6, 6) computes \sqrt{(6^2 + 6^2)} ≈ 8.485.

2. Error Handling in hypot()

This example shows an error when an incorrect number of arguments is passed to the hypot() function (more than two arguments).

import math

# Use of hypot() function with incorrect number of arguments
try:
    print("hypot(3, 4, 6) : ", math.hypot(3, 4, 6))
    
except TypeError as e:
    print("Error:", e)

hypot(3, 4, 6) :  7.810249675906654

Explanation

• math.hypot() function takes only two arguments.
• Passing three arguments (3, 4, 6) will raise a TypeError because the function cannot handle more than two inputs.
• The try-except block catches the error and prints a message explaining the issue.

3. Hypotenuse Calculation Using Perpendicular and Base

Practical Application : Given perpendicular and base of a right angle triangle find the hypotenuse. Using Pythagorean theorem which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

This example demonstrates how to use the hypot() function to calculate the hypotenuse of a right triangle given the perpendicular and base.

from math import hypot

# Perpendicular and base
p = 3
b = 4

# Calculates the hypotenuse
print(hypot(p, b))

Hypotenuse is: 5.0

Explanation

• from math import hypot statement imports the hypot() function from the math module.
• The values of p (perpendicular) and b (base) are set to 3 and 4, respectively.
• hypot(p, b) function computes the hypotenuse using the Pythagorean theorem: \sqrt{(p^2 + b^2)}.