Introduction
A hypotenuse is the longest side of a right triangle. It sits across from the 90-degree angle. To find its length, you use the Pythagorean theorem: c = √(a² + b²). You just need to know the two shorter sides, called legs.
This hypotenuse calculator does the math for you in seconds. Enter the lengths of side a and side b, and it gives you the hypotenuse, the area, the perimeter, and all three angles of the triangle. It also draws a diagram and shows each step of the solution so you can follow along and learn how the formula works.
Whether you are solving a homework problem, measuring a diagonal, or checking if a corner is square, this tool makes it fast and simple. Pick a quick example or type in your own numbers to get started.
How to Use Our Hypotenuse Calculator
Enter the two shorter sides of a right triangle below. The calculator will find the hypotenuse, area, perimeter, angles, and show you a diagram with a full step-by-step solution.
Side a (Vertical): Type the length of the first leg of your right triangle. This must be zero or greater.
Side b (Horizontal): Type the length of the second leg of your right triangle. This must be zero or greater.
Quick Examples: Click any preset button like "3 – 4 – 5" to load a common right triangle and see results right away.
Unit: Pick a unit of measurement such as cm, m, in, or ft. You can also leave it set to "No unit."
Output Precision: Choose how many decimal places you want in your answer. Pick "Exact" to see simplified square root form, "2 Dec" for two decimal places, or "3 Dec" for three.
Angle Unit: Choose "Degrees" to see angles in degrees or "Radians" to see them in radians.
Show Pythagorean Squares: Check this box to display a diagram of the squares built on each side of the triangle. This shows how a² + b² = c² works visually.
Show Step-by-Step Solution: Check this box to see every step of the Pythagorean theorem worked out from start to finish.
Calculate: Press this button to run the calculation. Results also update automatically as you type.
Reset: Press this button to clear your inputs and set everything back to the default values.
What Is the Hypotenuse of a Triangle?
The hypotenuse is the longest side of a right triangle. It is always the side that sits across from the 90-degree angle. Every right triangle has exactly one hypotenuse and two shorter sides called legs.
How to Find the Hypotenuse
You can find the hypotenuse using the Pythagorean theorem. This famous math rule says that in any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Written as a formula, it looks like this:
c = √(a² + b²)
Here, a and b are the two legs, and c is the hypotenuse. To use it, square each leg, add those two numbers together, then take the square root of the result. For example, if one leg is 3 and the other is 4, you get c = √(9 + 16) = √25 = 5.
What Is a Pythagorean Triple?
A Pythagorean triple is a set of three whole numbers that fit the Pythagorean theorem perfectly. The most well-known triple is 3, 4, 5. Other common ones include 5-12-13, 8-15-17, and 7-24-25. These triples are helpful because the hypotenuse comes out to a clean whole number with no decimals.
Where Is This Used in Real Life?
People use the hypotenuse formula more often than you might think. Builders check if a corner is square by measuring a 3-4-5 triangle. Engineers use it to find the length of a brace or a ramp. You can even use it to figure out the diagonal size of a TV or phone screen. Any time you need to find a straight-line distance across a right angle, this formula does the job.