Find the hypotenuse or a missing leg of a right triangle with a² + b² = c².
Calculated instantly in your browser.
How do you calculate the hypotenuse using the Pythagorean theorem?
a² + b² = c². The hypotenuse c = √(a² + b²); a missing leg b = √(c² − a²). Legs 3 and 4 give a hypotenuse of √(9 + 16) = √25 = 5 — the classic 3-4-5 triangle. The theorem only applies to right-angled triangles, and the hypotenuse is always the longest side, opposite the right angle.
Understanding your result
The theorem only applies to right-angled triangles. The hypotenuse is always the longest side, opposite the right angle. For full triangle solving (angles, area), use the Right Triangle Calculator.
Formula and method
a² + b² = c². The hypotenuse c = √(a² + b²); a missing leg b = √(c² − a²).
Worked example
Legs 3 and 4 give a hypotenuse of √(9 + 16) = √25 = 5 — the classic 3-4-5 triangle.
How to use this tool
- Choose whether to find the hypotenuse or a leg.
- Enter the two known sides.
- Read the missing side and the steps.
Common mistakes to avoid
- Using it on a triangle that has no right angle.
- Entering a hypotenuse shorter than a leg.
About the Pythagorean Theorem Calculator
The Pythagorean Theorem Calculator solves a² + b² = c² for a right-angled triangle. Enter two legs to get the hypotenuse, or the hypotenuse and one leg to get the missing leg.
Who should use this tool
Students, builders, designers and anyone working with right angles and distances.
Benefits
- Find the hypotenuse or a missing leg instantly.
- See the working, not just the answer.
- Also returns the triangle’s area.
- Private and instant.
Practical use cases
- Checking a corner is square on a building project.
- Finding a diagonal length.
- Solving geometry homework.
Frequently asked questions
What is the Pythagorean theorem?
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
Does it work for any triangle?
No — only right-angled triangles. For other triangles you need the law of cosines or sines.