Enter any two sides of a right triangle (two legs, or one leg and the hypotenuse) to instantly find the missing side using the Pythagorean theorem.
This tool calculates the length of any side of a right triangle using the Pythagorean theorem, given the other two sides. It's a fundamental tool in geometry, construction, navigation, and any field requiring right-angle measurements.
a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle) and a and b are the other two legs. To find a missing leg: a = √(c² − b²). To find the hypotenuse: c = √(a² + b²).
Enter any two known sides of a right triangle, and the calculator returns the length of the third side using the Pythagorean theorem.
Example 1: A right triangle with legs 3 and 4 has a hypotenuse of √(3² + 4²) = √25 = 5 — the classic "3-4-5" right triangle.
Example 2: A right triangle with hypotenuse 10 and one leg 6 has the other leg equal to √(10² − 6²) = √64 = 8.
Does this only work for right triangles? Yes, the Pythagorean theorem specifically applies only to right triangles (triangles with one 90-degree angle); other triangle types require different formulas like the Law of Cosines.
What is the hypotenuse? The hypotenuse is the longest side of a right triangle, always located opposite the right angle.
What are common real-world uses of the Pythagorean theorem? It's used in construction to check that corners are square, in navigation to calculate direct distances, in TV and monitor sizing (diagonal screen measurements), and in basic surveying and carpentry.
What are Pythagorean triples? These are sets of three whole numbers that satisfy a² + b² = c², like 3-4-5, 5-12-13, and 8-15-17 — useful shortcuts for checking right angles without calculating square roots.
Can this calculator find an angle, not just a side length? The basic Pythagorean theorem only solves for side lengths; finding an angle typically requires trigonometric functions like sine, cosine, or tangent in addition to this formula.