Pythagorean Theorem Calculator

Free Pythagorean Theorem Calculator for Students

Using a Pythagorean Theorem Calculator to Solve Problems

Our free Pythagorean Theorem Calculator uses the formula a² + b² = c² (where a and b are the lengths of a right triangle and c is the hypotenuse), as shown in Figure 01 below. Note that the Pythagorean Theorem only applies to right triangles (i.e. a triangle that has one 90-degree angle).

As long as you know the lengths of two legs (sides a and b) of a right triangle, you can use the Pythagorean Theorem calculator to determine the approximate length of the hypotenuse (side c).

While using our Pythagorean Theorem calculator is a great way to make fast and accurate calculations and to check your work, it is important for students to understand how to use the formula, a² + b² = c², to solve problems involving right triangles on their own.

In the section below, we will work through a practice problem where we will use the Pythagorean Theorem to calculate the length of the hypotenuse of a right triangle. Then, we will use the Pythagorean Theorem calculator to verify whether or not our answer is correct.

Pythagorean Theorem Calculator: How Does it Work?

Let’s go ahead and work through a practice problem that will help us to understand how to Pythagorean Theorem Calculator works (and how to use a² + b² = c² to solve problems without the use of a calculator).

Example #1: Find the Value of X

For this example, we are given a right triangle where two side lengths are given and the missing side is labeled using the variable x.

To solve this problem, we have to use the given information (and our knowledge of right triangles) to find the value of x.

By looking at the diagram in Figure 02, we can see that:

• The legs of the right triangle (a and b) are 7 and 9

• The hypotenuse of the right triangle (c) is x

So, we can use the Pythagorean Theorem formula, a² + b² = c², to solve for x, where:

• a=7

• b=9

• c=x

Now, we input a, b, and c into the Pythagorean Theorem Formula and solve as follows:

• a² + b² = c²

• 7² + 9² = x²

• 49 + 81 = x²

• 130 = x²

• √(130) = √(x²)

• 11.40175 = x

In this case, we will round our answer to the nearest hundredths decimal place, and we can conclude that:

Final Answer: x = 11.40

In other words, a right triangle with legs (a and b) that measure 7 and 9 has a hypotenuse (c) that measures approximately 11.40 units.

Of course, we can use the Pythagorean Theorem calculator at the top of this page to verify that our answer is correct. You can go ahead and input 7 for a and 9 for b into the calculator, and you will see that the result is that c=11.40, which confirms that our answer is correct!

Now, let’s get some more practice with solving problems using the Pythagorean Theorem by working through one more practice problem.

So, a right triangle with legs with measures 11.1 and 14.7 has a hypotenuse whose length is approximately 18.42 units.

You can verify this answer by using the Pythagorean Theorem Calculator at the top of the page, and you can continue using it to solve right triangle problems where you are given the lengths of a and b and tasked with finding the value of c.

Need More Practice with the Pythagorean Theorem?

If you are looking for more practice problems and/or more opportunities to use our free Pythagorean Theorem calculator, then check out our additional resources on this topic, including our step-by-step animated tutorial as well as a free collection of Pythagorean Theorem PDF practice worksheets (with complete answer keys) that you can download and print.

The more experience you have with using the Pythagorean Theorem, the better you will become at solving problems involving right triangles, which is an important skill that will be useful at all levels of math.

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