Missing Leg Calculator (b = √(c² − a²))

This page opens the Pythagorean theorem calculator in leg mode: you know one leg and the hypotenuse, and the theorem is rearranged into b² = c² − a². For a leg of 5 under a hypotenuse of 13 the steps read 13² − 5² = 169 − 25 = 144, so b = √144 = 12 — the 5-12-13 triple completed.

When the difference of squares is not a perfect square, the result is factorized and given as an exact simplified radical next to its decimal value, and the calculator refuses impossible input: the hypotenuse must always be the longest side, so c ≤ a is reported as an error rather than silently producing nonsense.

Finding a leg is the everyday inverse problem: how high a ladder of known length reaches at a given base distance, how far a brace must anchor from a wall, what vertical rise a sloped run hides. The result comes with the triangle's area, perimeter and a scaled diagram; and when no side is opposite a right angle at all, the general triangle calculator on this site takes over.