Right Triangle Calculator

A right triangle has exactly one 90° angle. The side opposite the right angle is the hypotenuse (always the longest side); the other two sides are the legs. The two non-right angles are acute (less than 90°) and always sum to 90°.

Two legs: when both perpendicular sides are known. Leg + hypotenuse: when one leg and the slanted hypotenuse are known. Leg + acute angle: when one leg and one non-right angle are known. Hypotenuse + acute angle: when the slanted hypotenuse and one non-right angle are known. Pick the mode that matches what you know.

The Pythagorean theorem calculator solves for one missing side when two sides are known. The right triangle calculator goes further: it returns all three sides, both acute angles, area, and perimeter, and it accepts angle inputs as well as side inputs. Use Pythagorean when you only need a single side; use this when you want the full picture.

Area = (leg a × leg b) ÷ 2. The two legs are perpendicular, so they serve directly as base and height. For legs 3 and 4, area = 6 square units. This is the same formula as a generic triangle with base × height ÷ 2, with the legs filling in.

The hypotenuse is opposite the largest interior angle (90°), so by the law of sines it is the longest side. If you enter a leg equal to or larger than the hypotenuse, the configuration is impossible and the calculator flags it.

An acute angle in a right triangle has to be strictly positive (the triangle would degenerate at 0°) and strictly less than 90° (the right angle already takes 90°). Values at the boundary give degenerate shapes with no triangle at all.