Pythagorean Theorem
Calculate the hypotenuse or missing leg of any right triangle using the Pythagorean theorem (a² + b² = c²).
Pythagorean Theorem: a² + b² = c²
Solve right triangles instantly
Result
About Pythagorean Theorem Calculator
Calculate the hypotenuse or missing leg of any right triangle using the Pythagorean theorem. Perfect for students, carpenters, architects, and anyone working with triangles.
Formula
a² + b² = c²
Where c is the hypotenuse (longest side), a and b are the legs
Pythagorean Triples (Integer Solutions)
| a | b | c (hypotenuse) |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 6 | 8 | 10 |
| 7 | 24 | 25 |
| 8 | 15 | 17 |
| 9 | 12 | 15 |
| 9 | 40 | 41 |
Frequently Asked Questions
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides. Formula: a² + b² = c², where c is the hypotenuse (longest side). Named after Greek mathematician Pythagoras (570-495 BCE).
If you know both legs (a and b), use: c = √(a² + b²). Example: a=3, b=4 → c = √(9+16) = √25 = 5. This is the classic 3-4-5 right triangle, often used in construction for checking right angles.
If you know the hypotenuse and one leg: a = √(c² - b²). Example: c=5, b=4 → a = √(25-16) = √9 = 3. This formula works for any right triangle where you know two sides.
A Pythagorean triple is a set of three integers that satisfy a² + b² = c². Common triples: 3-4-5, 5-12-13, 7-24-25, 8-15-17, 9-40-41. These are useful in geometry problems and construction.
Check if a² + b² = c² (where c is the longest side). If true, it's a right triangle. Example: sides 6,8,10 → 36+64=100 → 100=100 → Yes, it's a right triangle.
About the Pythagorean Theorem
Calculate the hypotenuse or missing leg of any right triangle using the Pythagorean theorem (a² + b² = c²).
Formula
Reference Table
| Category | Value |
|---|---|
| 3 | 4 |
| 5 | 12 |
| 6 | 8 |
| 7 | 24 |
| 8 | 15 |