Hypotenuse Calculator

The hypotenuse is the longest side of a right triangle, opposite the right angle.

How the Math Works

The hypotenuse calculator uses the fundamental Pythagorean theorem, which states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. By inputting the lengths of the two legs (a and b), the calculator computes c by taking the square root of (a² + b²). This mathematical relationship has been proven to hold true for all right triangles, making it one of the most reliable formulas in geometry.

Practical Applications

To use this calculator practically, simply enter the lengths of the two perpendicular sides of your right triangle. For example, if you're constructing a ramp that rises 3 feet vertically and extends 4 feet horizontally, inputting a=3 and b=4 will yield a hypotenuse of 5 feet, giving you the exact diagonal distance needed for materials. The calculator handles the computation instantly, eliminating manual calculation errors and saving time in construction, engineering, or design projects.

Day-to-Day Use

This calculation proves useful in everyday scenarios like determining the shortest path between two points when walking around a block, checking if furniture will fit diagonally in a room, or verifying ladder placement against a wall. Whether you're DIY enthusiasts hanging a TV mount, planning a garden layout, or simply curious about the diagonal measurement of your smartphone screen, the hypotenuse calculator provides quick, accurate results that help make informed decisions in daily life.

Worked example

Legs 5 and 12 → hypotenuse √169 = 13.

FAQ