Pathagoras’s theorem is used to calculate the height of a hypotenuse. It is an equation that connects the two sides of the right triangle. There are two shorter sides which are also known as legs and one longer side which is known as hypotenuse. This equation is known as Pythagorean theorem, often known as Pythagoras’ theorem.


Remember that a right triangle has a 90-degree angle. Since the sum of the angles of any triangle equals 180. The other two angles are 90 degrees which completes it. In this article, we will understand the fundamentals of the triangle. We will also cover the process of the Pythagorean Theorem Calculator.


The Pythagorean Theorem: What is it?

The Pythagorean theorem explains the relationship between a right triangle’s three sides. The square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs. This theorem is also known as the hypotenuse formula. The formula is as follows if a right triangle has a hypotenuse of c and legs of a and b.


a² + b² = c²

Pythagoras, a sixth-century BC Greek mathematician and philosopher, was credited with developing the theorem. The theorem was first applied by the Babylonians and Indians, but Pythagoras (or his disciples) is credited with proving it. It is important to remember that there is no hard proof that Pythagoras developed or proved this theorem.

What is the Pythagorean Theorem Used for?

The Pythagorean theorem is as follows:


Enter both of your lengths into the formula. Assume, for illustration purposes, that the hypotenuse (c) is 8.94 and one leg (a) equals 4. Our goal is to measure the leg’s length.

Following the input of the variables into the calculation, we obtain 4² + b² = 8.94².

  • To get 16 + b² = 80, square each term.
  • Put related terms together to obtain b² = 64.
  • To find b = 8, take the square root of both sides of the equation. Use an online Pythagorean theorem calculator to verify it now!


Keep in mind that before combining like terms and computing the square root, you should rearrange the equation to isolate the appropriate variable if you are solving for an or b.


The method we showed above is how the Pythagorean theorem calculator will find the sides. If you would rather do things by hand, we have provided the approach to demonstrate how you might resolve your issue.

What Formula is the Hypotenuse?

The Pythagorean theorem is simply used in the hypotenuse formula to find the hypotenuse, c.


We just need to take the square root of each side of the equation a² + b² = c² and solve for c to find the hypotenuse. As a result, we have c = √(a² + b²). This is sometimes referred to as the hypotenuse formula and is nothing more than a reformulation of the Pythagorean theorem.

Other Things to Think About When Working with Triangles

A triangle’s sides can be seen to have varying degrees of slope or gradient. The slope of each side can be ascertained using the slope calculator. The slopes of the sides that make up the right angle in a right triangle have products with values of -1. If you would like to compute the slope manually, the formula is as follows:


(x₃ – x₁) / (y₃ – y₁)


The right triangle calculator can also be used to determine the angles and side lengths that are lacking from a right triangle. Use our angle converter if the angles in the problem are in degrees and you need to convert them to radians or vice versa. Converting radians into degrees and degrees into radians is simple.


There could occasionally be an issue with two lengths missing. In these situations, the Pythagorean theorem calculator is useless; instead, trigonometric functions must be used to find the missing parts. Do not fret! You can use our amazing calculator for trigonometric functions. If the lengths of the other two sides are known, the Pythagorean theorem can be applied to solve any side.


The length of the hypotenuse squared equals the total of the squares of each leg, according to the Pythagorean theorem.

  • How to Apply Right Triangles to the Pythagorean Theorem
  • The Pythagorean theorem is used to get the length of the third side of a right triangle given the lengths of any two of its sides. To solve, substitute the two known values for the values of a, b, or c in the formula and solve the problem.

Use of Calculators

The Pythagorean Theorem equation can be solved using this calculator for sides an orb or hypotenuse c. The triangle’s hypotenuse is the side that faces away from the right angle. To find the third, enter any two values for right triangles only. View the step-by-step solution with the Pythagorean Theorem formula. The area A of the right triangle with sides A and b is also found by this calculator. 

Pythagorean Triples: What Are They?

A set of three positive integers with sides a and b and hypotenuse c that fulfill the Pythagorean Theorem formula a2 + b2 = c2 is known as a Pythagorean triple. 3, 4, and 5 are the smallest known Pythagorean triples.


The Pythagorean equation bears the name of Pythagoras, an ancient Greek scholar. This relationship is helpful because the Pythagorean theorem can be used to calculate the length of the third side of a right triangle if the lengths of the first two sides are known.