Pythagorean Theorem
Calculate the hypotenuse of a right triangle using the Pythagorean theorem. Get instant step-by-step solutions — completely free, no signup required.
Free Pythagorean Theorem Calculator
Enter your problem below to get an instant step-by-step solution.
About Pythagorean Theorem
Calculate the hypotenuse of a right triangle using the Pythagorean theorem. Geometry explores the properties and relationships of shapes, sizes, and dimensions. From basic triangles to 3D solids, geometric formulas are used in engineering, architecture, and physics.
Our Pythagorean Theorem calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any pythagorean theorem expression and receive a complete, verified solution with every step shown.
Pythagorean Theorem Formula
a² + b² = c²
In any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Use it to find a missing side, check whether a triangle is right-angled, or find the distance between two points.
Worked Example
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
- Substitute: c² = 6² + 8²
- Square: c² = 36 + 64 = 100
- Take the square root: c = √100
Answer: c = 10 cm
Common Mistakes to Avoid
- Adding the squares when the unknown is a leg — then subtract: a² = c² − b².
- Using the theorem on a triangle with no right angle.
- Forgetting to take the square root at the end.
How to Use the Pythagorean Theorem Calculator
- 1
Type your Pythagorean Theorem problem into the input field above
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Press Enter or click the Solve button to run the calculation
- 3
Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Pythagorean Theorem formula?
a² + b² = c². In any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Use it to find a missing side, check whether a triangle is right-angled, or find the distance between two points.
Can you show a worked Pythagorean Theorem example?
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.: Substitute: c² = 6² + 8²; Square: c² = 36 + 64 = 100; Take the square root: c = √100. Answer: c = 10 cm.
Is this Pythagorean Theorem calculator free to use?
Yes — the Pythagorean Theorem calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Pythagorean Theorem homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.