Area of a Right Triangle Calculator

A right triangle has one angle measuring exactly 90 degrees. The two sides that meet at this right angle are perpendicular, so either can serve as the base while the other serves as the height. Its area is A = (b × h) / 2. This is half the area of a rectangle with the same base and height because two congruent right triangles fit together to make that rectangle. For a triangle with base 3 and height 4, multiply the perpendicular sides to get 12, then divide by two to get an area of 6 square units. The order of the legs does not matter. However, the slanted hypotenuse should not be entered as the height unless it happens to be perpendicular to the selected base, which it is not in a standard right triangle. Correctly identifying the two legs is the most important step. The calculator uses the Pythagorean theorem to find the missing hypotenuse. If the legs are b and h, the hypotenuse c is the square root of b² + h². It then adds all three side lengths for the perimeter. In the familiar 3-4-5 triangle, the hypotenuse is 5 and the perimeter is 12. These related values help with roof slopes, ramps, diagonal bracing, surveying, navigation, and construction layouts. Measurements should use one consistent unit. Legs measured in centimeters produce a hypotenuse and perimeter in centimeters, while area is reported in square centimeters. If one leg is in meters and the other is in centimeters, convert them before calculating. The numerical display does not attach units because the calculator cannot know which unit you measured; apply the correct linear or square unit to each result. Right triangle area is also useful for shapes that can be decomposed into triangles. A rectangle cut along a diagonal makes two equal right triangles. Irregular floor plans, plots of land, and coordinate geometry polygons can often be split into right triangles, calculated separately, and summed. This approach turns a complex outline into repeated applications of a simple formula. Decimal values are accepted for precise measurements. Keep enough significant digits during calculation and round the final answer according to the precision of the measured sides. The area depends on both measurements, so an error in either leg affects the product. For classroom work, the exact expression may be preferred when a hypotenuse contains a square root, while the calculator supplies a practical decimal result for direct use.