# Pythagorean Theorem Calculator

Enter the values to calculate the length of the third side of a right-angled triangle using this Pythagorean / Pythagoras Theorem Calculator.

• Formula:
c = a2 + b2

## Pythagoras Theorem Calculator

Pythagoras theorem calculator helps to find the length of the unknown side of the right-angled triangle by using the Pythagorean theorem.

It solves the equation for side a, b, or c and calculates the final result with one click.

## What is Pythagorean Theorem?

This theorem describes how all three sides of a right triangle are connected in Euclidean geometry.

Pythagoras Theorem states that the sum of the squares of the two sides of a right triangle equals to the square of the hypotenuse.

The hypotenuse is opposite to 90° and it is considered as the longest side in a right triangle.

## Pythagorean Theorem Formula

According to the above definition, the Pythagorean equation is:

Hypotenuse2 = Perpendicular2 + Base2

Or

c2 = a2 + b2

Where,

c is the hypotenuse,

b refers to the opposite side of the hypotenuse.

The Pythagorean Theorem solver uses the above formula to find the length of the unknown side of the right triangle.

## How to find an unknown Side of a Right Triangle?

The Pythagorean Theorem solver uses the above formula to find the length of the unknown side of a right triangle.

To find the length of the hypotenuse ‘c’, it uses the below equation:

c = √(a² + b²)

To calculate the length of the side ‘a’, it uses the below equation:

a = √(c² - b²)

And to solve the length of the side ‘b’, it uses the following equation:

b = √(c² - a²)

Example:

Consider the smallest Pythagoras triple as a=4, b=3. Calculate the unknown side of the right-angle triangle.

Step 1: Use the Pythagorean Theorem equation.

c2 = a2 + b2

Step 2: Enter the values into the equation.

c2= 42 + 32

Step 3: Complete the calculations.

c2 = 16 + 9

c2 = 25

Take square root on both sides.

c2 = 25

c = 5

Note: Pythagorean triples are the set of three integers that satisfy the Pythagoras theorem.

### References:

1. What is Pythagorean theorem | Wikipedia