Heron's Formula Calculator

Heron's formula gives you the area of any triangle when you know its three side lengths, with no need to measure an angle or a height. It was described by the ancient Greek mathematician Heron of Alexandria in the first century and remains one of the most practical tools in geometry because side lengths are almost always easier to measure than the perpendicular height. The method works in two steps. First you calculate the semi-perimeter, which is simply half the sum of the three sides: s = (a + b + c) / 2. Then you plug that into the area formula: area = the square root of s times (s minus a) times (s minus b) times (s minus c). The result only exists as a real number if the three sides satisfy the triangle inequality, meaning each side must be less than the sum of the other two. If that condition is not met, the expression under the square root is negative and no valid triangle exists. This calculator handles that check automatically and displays an error if the inputs are invalid. Enter the three side lengths in any consistent unit, whether centimetres, metres or anything else, and the calculator returns the area in square units of the same measure, the semi-perimeter, the full perimeter, and a classification of the triangle as equilateral, isosceles or scalene. The tool suits students, tradespeople estimating material quantities, and anyone needing to find an area from a measured outline. Results are for reference only.

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