Hypotenuse Calculator

About this calculator

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two legs: c = √(a² + b²). This is one of the oldest and most widely proven results in mathematics, with independent proofs going back to ancient Babylonian, Chinese and Greek mathematics, and it holds true for every right triangle regardless of its specific proportions.

Beyond geometry class, the hypotenuse formula is a daily working tool in carpentry and construction — framers use it to cut roof rafters and stair stringers to the correct diagonal length, and the "3-4-5 rule" (a triangle with legs 3 and 4 always has a hypotenuse of 5) is a standard trick builders use to square up corners without any angle-measuring tool. It's equally essential in navigation and surveying for calculating direct-line distances from two perpendicular measurements, and in physics for resolving vector components back into a resultant magnitude.

This calculator takes the two legs of a right triangle and returns the hypotenuse along with the triangle's area, so you get the full picture of the triangle from just two measurements.