# Pythagorean Theorem Calculator

Welcome to the Pythagorean theorem calculator. This Pythagorean calculator **finds the missing side of a triangle** as long as you're dealing with a **right triangle**.

Additionally, with this Pythagorean theorem calculator, **you can calculate the perimeter of any right triangle and its area**. If you want to calculate the area of any triangle (and not only right triangles), use our triangle area calculator.

The Pythagorean theorem is the basis for more advanced topics:

- For example, the relationship between trigonometric functions sine and cosine (
`sin²x + cos²x + 1`

) comes from applying the Pythagorean theorem. - If you're dealing with vector addition, the Pythagorean theorem will tell you the
**resultant vector magnitude**. For example, when finding the resultant velocity or acceleration.

## Pythagorean theorem formula

Pythagorean theorem states that **"the square on the hypotenuse equals the sum of the other two squares."**

The Pythagorean theorem equation is:

`a² + b² = c²`

where

`a`

is a side of the right triangle;`b`

is another side of the right triangle;`c`

is the hypotenuse.

From that Pythagorean theorem equation, you **solve for any of the sides**:

`c = √(a² + b²)`

`a = √(c² - b²)`

`b = √(c² - a²)`

From the previous equation, we can also deduct one of the most important rules of square triangles: **None of the sides ( a or b) can be greater than the hypotenuse c**.

## Calculating the area of a right triangle

To calculate the area of a right triangle, use the following formula:

`Area = a×b/2`

## Calculating the perimeter of a right triangle

The perimeter of a triangle is simply the sum of its three sides:

`perimeter = a + b + c`

## How to use this Pythagorean theorem calculator

**Fill in the lengths of any two sides**(c being the hypotenuse), and this Pythagorean calculator will evaluate the third one.- You can also
**input the area and one of the triangle sides (**, and the Pythagorean theorem calculator will find the other missing variables.`a`

or`b`

)

Let's look at how to use this calculator through an example. Suppose you know `a = 8`

, `b = 16`

, and want to find the hypotenuse. Follow these steps:

- Input
`a = 8 cm`

into the first box of the calculator. - Input
`b = 16 cm`

into the second box of the calculator. - The answer should be
`17.89 cm`

. That's how you use this calculator to find the missing side of a triangle.

You can verify the result using the Pythagorean theorem equation: