Heron's Formula Calculator

Heron's formula calculates the area of any triangle from just its three side lengths — no angles or heights required. The formula is: Area = √[s(s-a)(s-b)(s-c)], where a, b, c are the side lengths and s is the semiperimeter (half the perimeter).

Heron of Alexandria was a Greek mathematician and engineer who lived around 10–70 CE. He proved the formula in his work "Metrica," though there's evidence Archimedes knew it earlier. It's one of the oldest non-trivial geometry results still in everyday use.

Use base × height when you already know one side and the perpendicular height to it — it's simpler. Use Heron's formula when you only know the three side lengths and don't have any heights or angles to work with. It's the go-to method for SSS triangle area.

The semiperimeter (s) is half the triangle's perimeter: s = (a + b + c) / 2. It appears in Heron's formula and in formulas for the inradius, exradii, and other geometric quantities. It's a useful shortcut to keep the formula compact.

Yes — for any valid triangle (one that satisfies the triangle inequality: each side must be less than the sum of the other two). It works for acute, right, obtuse, scalene, isosceles, and equilateral triangles alike.

It can lose precision for nearly-degenerate "needle" triangles where one side is almost equal to the sum of the other two. For those cases, a numerically-stable variant (Kahan's reformulation) is preferred. For typical inputs the standard formula is plenty accurate.