Pythagorean Theorem Calculator
Solve a² + b² = c² step by step: find the hypotenuse from two legs, find a missing leg, or test whether three sides form a right triangle — with exact simplified radicals like 5√2, a scaled diagram, area and perimeter.
Result
The Pythagorean theorem says that in a right triangle the two legs and the hypotenuse are locked together by a² + b² = c². This calculator does all three jobs that follow from it: finds the hypotenuse when both legs are known, finds a missing leg when one leg and the hypotenuse are known, and checks whether three given sides form a right triangle at all. Each run prints the substitution line by line — 3² + 4² = 9 + 16 = 25, c = √25 = 5 — the way you would write it out by hand.
Exactness is the point. When the square root does not come out whole, the radicand is factorized into primes and every square factor is pulled out, so legs of 5 and 5 give the hypotenuse as the exact value 5√2 first and the decimal ≈ 7.0711 second. Decimal inputs are scaled to whole numbers before squaring, which is why 1.5 and 2 produce exactly 2.5 rather than a rounded approximation, and the right-triangle check compares the squares as exact integers — 5, 12, 13 passes because 25 + 144 equals 169 precisely.
Beyond the missing side you also get the area (half the product of the legs), the perimeter, and an SVG diagram of your right triangle drawn to scale with the right angle marked — enough to sanity-check a ladder length, a diagonal brace, a TV screen or a fence corner in one run.
The theorem only speaks about right triangles. When your triangle has no 90° angle — or you know a mix of angles and sides — the general triangle calculator on this site solves it with the law of sines and cosines and reports every side, angle, height and the area. Both tools run locally in your browser: nothing is uploaded and there is no registration.