Hypotenuse Calculator

The hypotenuse is the longest side of a right triangle and always lies opposite the ninety-degree angle. The Pythagorean theorem states that the square of the hypotenuse equals the sum of the squares of the two perpendicular legs. If the legs are called a and b and the hypotenuse is c, the relationship is a squared plus b squared equals c squared. This calculator rearranges that single equation to solve either type of missing side. To find the hypotenuse, square both known leg lengths, add the squares, and take the square root. A triangle with legs 3 and 4 has a hypotenuse equal to the square root of 9 plus 16, which is 5. To find a missing leg, square the hypotenuse, subtract the square of the known leg, and take the square root. A triangle with hypotenuse 13 and one leg 5 therefore has a missing leg of 12. The theorem applies only to right triangles. It does not directly solve an oblique triangle with no ninety-degree angle; those cases require the law of cosines or other measurements. In missing-leg mode, the entered hypotenuse must be greater than the known leg. Equal values would produce a zero-length side, and a shorter proposed hypotenuse would make the squared difference negative, neither of which forms a valid triangle. Right-triangle calculations are useful in construction, surveying, navigation, computer graphics, and everyday measurement. A builder can check whether a rectangular corner is square with a 3-4-5 layout. A screen's diagonal follows the same theorem from its width and height. The straight-line distance between horizontal and vertical coordinate changes is also a hypotenuse. In three dimensions, the idea can be applied repeatedly to combine perpendicular distances. Use the same unit for both inputs. The output then uses that length unit as well, whether it is centimeters, meters, inches, feet, or another unit. The calculator retains full numeric precision during the square and square-root operations and rounds the displayed value to eight decimal places. Exact integer results are shown without unnecessary trailing zeros, making both common Pythagorean triples and decimal measurements easy to read.