Heron's Formula Calculator

Heron's formula calculates the area of a triangle using only the lengths of its three sides, denoted as a, b, and c. First, the calculator determines the semi-perimeter (s) by adding all three side lengths together and dividing the sum by two: s = (a + b + c) / 2. Next, it applies the core equation: Area = square root of [s * (s - a) * (s - b) * (s - c)]. The perimeter is simultaneously computed as the direct sum of the three side lengths (a + b + c).

Imagine you have a triangular plot of land with side lengths of 7 meters, 9 meters, and 12 meters. First, find the semi-perimeter s by adding the sides together and dividing by 2: s = (7 + 9 + 12) / 2 = 28 / 2 = 14 meters. Next, substitute s and the side lengths into Heron's area formula: Area = square root of [14 * (14 - 7) * (14 - 9) * (14 - 12)]. This simplifies to the square root of [14 * 7 * 5 * 2], which equals the square root of 980, yielding an approximate area of 31.30 square meters. The perimeter is simply 7 + 9 + 12 = 28 meters.

Always verify the triangle inequality theorem before running your numbers—the sum of any two side lengths must strictly exceed the remaining third side, otherwise a valid triangle cannot exist. Double-check your measurement units to ensure all three sides share the same unit of length to avoid skewed area calculations.