Free Online Pythagorean Theorem Calculator

1. Pick the side you want to solve for: hypotenuse c, leg a, or leg b.
2. Type the two known side lengths into the labelled inputs.
3. Read the computed value of the missing side along with the formula used.

The Pythagorean theorem is the cornerstone of plane geometry: in any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Knowing two sides lets you compute the third.

Three rearrangements cover every case. To find the hypotenuse c from legs a and b: c = √(a² + b²). To find a leg given the hypotenuse c and the other leg: a = √(c² − b²) or b = √(c² − a²). This tool handles all three with a mode selector.

Validation catches impossible triangles — if you claim c ≤ a or c ≤ b, the hypotenuse isn't the longest side and the inputs are rejected. Applications are everywhere geometry meets the real world: construction (squaring a foundation), navigation (straight-line distance), graphics (sprite hit detection), and physics (resolving vectors into perpendicular components).