Hypotenuse Calculator
Find the hypotenuse or a missing leg of any right triangle using the Pythagorean theorem. Enter two known sides and the calculator handles the rest. A classic 3-4-5 right triangle has legs of 3 and 4, giving a hypotenuse of 5.
The Pythagorean Theorem
For any right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Rearranged to find the hypotenuse: c = sqrt(a² + b²). To find a missing leg: a = sqrt(c² - b²).
Example: Finding the Hypotenuse
If the two legs are 6 and 8: c = sqrt(6² + 8²) = sqrt(36 + 64) = sqrt(100) = 10
Example: Finding a Missing Leg
If the hypotenuse is 13 and one leg is 5: a = sqrt(13² - 5²) = sqrt(169 - 25) = sqrt(144) = 12
Common Pythagorean Triples
Some right triangles have all-integer side lengths. The most well-known:
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
Any multiple of these also works (e.g., 6, 8, 10 is just 2 times the 3-4-5 triple).
Perimeter and Area
The perimeter of a right triangle is simply a + b + c. The area is (1/2) x a x b, since the two legs serve as base and height.