Pythagorean Theorem Calculator

If you’re working with right triangles and want to calculate the length of a side or check if three numbers make a right triangle, the Pythagorean Theorem Calculator is your go-to tool. Whether you’re a student, teacher, or just someone brushing up on geometry, this calculator makes solving a² + b² = c² quick and easy.

What Is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical principle used to find the length of a side in a right-angled triangle. The formula is:

• a² + b² = c²

Where:

• a and b are the lengths of the two shorter sides (legs),
• c is the hypotenuse (the longest side, opposite the right angle).
• This formula only works for right-angled triangles.

How the Pythagorean Theorem Calculator Works

Our calculator lets you input any two known side lengths of a triangle and instantly find the third. It works in all the following cases:

• Solve for a, b, or c
• Check if three numbers form a right triangle
• Help you visually understand triangle properties

Simply enter two values, click “Calculate,” and get the missing side—along with a breakdown of the solution steps.

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How to Solve the Pythagorean Theorem?

To solve it manually:

• Square the two known sides.
• Add them (if solving for the hypotenuse), or subtract (if solving for a leg).
• Take the square root of the result.

Example:

• If a = 3 and b = 4, then
• 3² + 4² = 9 + 16 = 25
• √25 = 5, so c = 5

Common Questions Answered (Based on Search Trends)

What is the full Pythagorean formula?

It’s a² + b² = c², where c is always the hypotenuse.

How do I find the missing side of a triangle?

Use the calculator:

• If you know a and b, find c by √(a² + b²)
• If you know c and a, find b by √(c² – a²)

What is the Pythagorean Theorem for dummies?

Think of it as a shortcut to find the third side of a right triangle.

How to calculate Pythagoras step by step?

• Identify if it’s a right triangle.
• Label your sides as a, b, and c.
• Plug into a² + b² = c².
• Solve accordingly.

How do you use Pythagorean theorem on a calculator?

Use a² + b² = c² or rearrange it depending on the side you’re solving for. Our tool automates this process.

How to Tell if 3 Numbers Make a Right Triangle?

Plug the three numbers into the Pythagorean formula:

• Assign the largest number as c (hypotenuse).
• Check if a² + b² = c².

Examples:

• Does 6, 8, 10 make a right triangle?
  Yes, because 6² + 8² = 36 + 64 = 100 → √100 = 10
• Does 5, 12, 13? Yes.
• Does 3, 4, 6? No

Exploring Number Sets and Right Triangles

• Is 3-4-5 a trick? Yes, it’s a common Pythagorean triple.
• Is 6, 8, 10 a right triangle? Yes.
• Is 5.6 a triangle side? Depends, but not a Pythagorean triple.
• Is 9-12-15 right? Yes—it’s a multiple of 3-4-5.

What Is 3 Squared Plus 4 Squared?

• That’s 3² + 4² = 9 + 16 = 25
  √25 = 5 → This proves 3, 4, and 5 form a right triangle.

How Do You Find A or B in Pythagorean Theorem?

Rearrange the formula:

To find a or b:

• a = √(c² – b²)
• b = √(c² – a²)

Use the calculator to avoid mistakes—it handles this instantly and accurately.

Using the Tool Without a Calculator

You can use mental math or pen and paper to follow the same rules:

• Memorize some common Pythagorean triples like 3-4-5, 5-12-13, 7-24-25
• Use basic arithmetic for squares and square roots
• Use trigonometry or algebra for complex questions

When Should I Use the Pythagorean Theorem?

• Geometry class
• Engineering and architecture
• Real-world measurements
• DIY or home improvement projects

Tool Features Recap

• Instantly calculates missing sides
• Verifies right triangle sets
• Step-by-step solutions
• Beginner-friendly
• Works on desktop and mobile

FAQs

What does it mean in math?

It’s a theorem used to relate the three sides of a right triangle.

Can you use it if it’s not a right triangle?

No—it only applies to right-angled triangles.

Is it a perfect square?

If a² + b² = c² results in a perfect square, then yes. Otherwise, the hypotenuse may be irrational.

Try the Pythagorean Theorem Calculator Now

Take the guesswork out of triangle calculations. Use the Pythagorean Theorem Calculator to instantly verify triangle properties or find unknown side lengths. Fast, easy, and accurate.