Pythagorean Theorem Calculator

The Pythagorean theorem describes the relationship among the three sides of a right triangle. If a and b are the legs that meet at the right angle and c is the hypotenuse opposite that angle, then a squared plus b squared equals c squared. This calculator rearranges that relationship to solve for whichever side is unknown. To find the hypotenuse, it adds the squares of both legs and takes the positive square root. To find a leg, it subtracts the square of the known leg from the square of the hypotenuse before taking the positive square root. The theorem applies only to right triangles. A right triangle contains one angle of exactly 90 degrees, and its hypotenuse is always its longest side. That longest-side rule is why a hypotenuse entered while solving for a leg must exceed the known leg. Lengths may use any unit, including centimeters, meters, inches, or feet, as long as both known values use the same unit. The calculated side then uses that same unit. Squared values are intermediate calculations; the final square root returns the answer to an ordinary length. This relationship is useful in geometry, construction, surveying, navigation, computer graphics, and everyday measurement. It can find a diagonal across a rectangular room, the length of a ladder needed to reach a height, or the direct distance represented by horizontal and vertical movement. Decimal inputs are supported, so the calculator also works with measured values rather than only textbook integers. Results are rounded to a practical number of decimal places while preserving enough precision for most learning and planning tasks. A result can be checked by squaring all three side lengths and confirming that the two leg squares add to the hypotenuse square. Some right triangles have whole-number sides, such as 3, 4, and 5, while many produce irrational square roots. An irrational result is expected and does not mean the triangle is invalid. For physical projects, retain extra decimal places during calculation and round only at the end according to the precision of the original measurements.