# Pythagorean theorem calculator

Hypotenuse (c) calculation:

 Enter leg (a): Enter leg (b): Hypotenuse (c) result:

Leg (a) calculation:

 Enter leg (b): Enter Hypotenuse (c): Leg (a) result:

Leg (b) calculation:

 Enter leg (a): Enter hypotenuse (c): Leg (b) result:

Here we discuss list of online math calculators that help us for doing calculation easily.

### Pythagorean Theorem

This calculator solves the Pythagorean Theorem equation for sides a or b, or the hypotenuse c. The Pythagorean Theorem, also known as Pythagoras' theorem, is a fundamental relation between the three sides of a right triangle. Given a right triangle, which is a triangle in which one of the angles is 90°, the Pythagorean theorem states that the area of the square formed by the longest side of the right triangle (the hypotenuse) is equal to the sum of the area of the squares formed by the other two sides of the right triangle.

In other words, given that the longest side c = the hypotenuse, and a and b = the other sides of the triangle:

a2 + b2 = c2

The hypotenuse is the side of the triangle opposite the right angle.For right triangles only, enter any two values to find the third. See the solution with steps using the Pythagorean Theorem formula.

This calculator also finds the area A of the right triangle with sides a and b. The formula for area of a right triangle is:

A=ab/2

How to Use the Pythagorean Theorem Calculator?

The procedure to use the Pythagorean Theorem calculator is as follows:

1. Enter the values of two sides in the input fields and enter “x” for the unknown side value

2. Click the button “Solve” to get the unknown side measure

3. The value of the variable “x” will be displayed in the output “x” field

What is the Pythagorean theorem?

The Pythagorean theorem describes how the three sides of a right triangle are related in Euclidean geometry. It states that the sum of the squares of the sides of a right triangle equals the square of the hypotenuse. You can also think of this theorem as the hypotenuse formula. If the sides of a right triangle are a and b and the hypotenuse is c, the formula is

a² + b² = c²

The theorem was credited to the ancient Greek philosopher and mathematician Pythagoras, who lived in the sixth century BC. Although it was previously used by the Indians and Babylonians, Pythagoras (or his students) were credited to be the first to prove the theorem. It should be noted that there is no concrete evidence that Pythagoras himself worked on or proved this theorem.

Example: How to use the Pythagorean theorem

1. Input the two lengths that you have into the formula. For example, suppose you know a = 4, b = 8 and we want to find the length of the hypotenuse c.

2. After the values are put into the formula we have 4²+ 8² = c²

3. Square each term to get 16 + 64 = c²

4. Combine like terms to get 80 = c²

.5. Take the square root of both sides of the equation to get c = 8.94.

The Pythagorean theorem calculator will solve for the sides in the same manner that we displayed above. We have included the method to show you how you can solve your problem if you prefer to do it by hand.

What is the hypotenuse formula?

The hypotenuse formula is simply taking the Pythagorean theorem and solving for the hypotenuse, c. Solving for the hypotenuse, we simply take the square root of both sides of the equation a² + b² = c²and solve for c. When doing so, we get c = √(a² + b²). This is just an extension of the Pythagorean theorem and often is not associated with the name hypotenuse formula.