Hypotenuse Calculator
Calculate the hypotenuse or missing sides of a right triangle using the Pythagorean theorem. Instantly find the area, perimeter, and angles of any right-angled triangle.
Right Triangle Solver
Solve for any missing side using a² + b² = c²
Select the side you want to calculate. The other two must be filled in.
Ensure all sides use the same unit before calculating.
Triangle Properties
Side lengths, area, perimeter, and angles
Fill in two of the three sides and click Calculate Triangle to solve the right triangle.
Common Pythagorean Triples
Integer side lengths that perfectly satisfy the Pythagorean theorem (a² + b² = c²).
| Side a | Side b | Hypotenuse c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 9 | 40 | 41 |
| 11 | 60 | 61 |
| 12 | 35 | 37 |
| 20 | 21 | 29 |
Hypotenuse Calculator FAQ
Everything you need to know about right triangles and the Pythagorean theorem.
The hypotenuse is the longest side of a right-angled triangle. It is always the side opposite the 90-degree (right) angle. The other two shorter sides are known as the legs or the adjacent/opposite sides relative to a given angle.
The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is written as: a² + b² = c².
To calculate the hypotenuse, you square the lengths of the two shorter sides (a and b), add those two results together, and then take the square root of the sum. The formula is c = √(a² + b²). For example, if a = 3 and b = 4, then c = √(9 + 16) = √25 = 5.
No, the hypotenuse is always the longest side of a right triangle. Because the formula is c² = a² + b², and both a and b are positive numbers, c² must be strictly greater than a² and strictly greater than b². Therefore, c must be greater than both a and b.
Pythagorean triples are sets of three positive integers (a, b, c) that perfectly satisfy the Pythagorean theorem a² + b² = c². The most famous example is (3, 4, 5). Other common triples include (5, 12, 13), (8, 15, 17), and (7, 24, 25). Any multiple of these triples (like 6, 8, 10) is also a valid Pythagorean triple.
If you know the hypotenuse (c) and one leg (a), you can find the other leg (b) by rearranging the Pythagorean theorem: b = √(c² – a²). If you know both legs (a and b), you find the hypotenuse using c = √(a² + b²). This calculator handles all these scenarios automatically.
The area of a right triangle is exactly half the product of its two shorter sides (the legs). The formula is Area = 0.5 × a × b. This is because the two legs act as the base and the height of the triangle, which are perpendicular to each other.
One angle is always 90°. To find the other two angles, you can use trigonometric ratios. If you know the side lengths, the angle opposite side ‘a’ can be found using the inverse tangent function: Angle A = arctan(a / b). The remaining angle is simply 90° – Angle A, since the sum of angles in any triangle is 180°.