# Pythagorean Theorem Calculator

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

## Pythagoras Theorem Calculator

### To use this calculator, select the side to calculate and, input values of the adjacent side and opposite sides

## Pythagoras Theorem Calculator

The calculator helps to find the length of the unknown side of the right-angled triangle by using the hypotenuse formula.

It solves the equation for side ** a, b,** or

**and calculates the final result with one click.**

*c*## What is Pythagorean Theorem?

The theorem describes that 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:

**Hypotenuse ^{2} = Perpendicular^{2} + Base^{2}**

Or

**c ^{2 }= a^{2} + b^{2}**

Where,

** c **is the hypotenuse,

** a **is an adjacent side,

** 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.

*c ^{2 }= a^{2} + b^{2} *

**Step 2: **Enter the values into the equation.

*c ^{2}= 4^{2} + 3^{2}*

**Step 3: **Complete the calculations.

*c ^{2} = 16 + 9*

*c ^{2}*

*= 25*Take square root on both sides.

*c = 5*

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

### References:

- Pythagorean theorem | Wikipedia