How to Find the Hypotenuse of a Right Triangle

The hypotenuse is the longest side of a right triangle. It is always located directly across from the 90-degree right angle. Finding its length is essential for calculating diagonal distances in construction, navigation, and mathematics.

You can calculate this instantly using our Right Angle Calculator Triangle tool, or follow the mathematical steps below.

The Hypotenuse Formula

To find the hypotenuse (labeled as c), you must know the lengths of the two perpendicular legs (labeled as a and b).

By taking the Pythagorean theorem (a² + b² = c²) and isolating c, we get the direct formula for the hypotenuse:

c = √(a² + b²)

Step-by-Step Example Calculation

Suppose you are cutting a rectangular piece of wood that is 6 inches wide (Leg a) and 8 inches tall (Leg b). You want to know the exact diagonal distance from one corner to the opposite corner (the hypotenuse).

1. Square Leg a: 6 × 6 = 36
2. Square Leg b: 8 × 8 = 64
3. Add them together: 36 + 64 = 100
4. Take the square root: √100 = 10

The hypotenuse is exactly 10 inches long.