Heron's Formula Calculator
Enter the three side lengths of a triangle to get its area straight from the sides — no height or angles required — together with the perimeter.
Area from three sides
Type in side a, side b and side c and the calculator returns the area via Heron's formula and the perimeter (a + b + c) at the same time.
It must be a real triangle
No side can be as long as the other two combined. Sides like 1, 1 and 5 cannot close into a triangle, so no area exists.
What is Heron's formula?
Triangle area from the sides
This Heron's formula calculator finds the area of a triangle when all you know is its three side lengths — no height, no angles. You measure the three sides, and Heron's formula does the rest. It works for every valid triangle: right-angled, acute, obtuse, scalene, isosceles, or equilateral. Named after Heron of Alexandria, who set it down in the first century AD, it is the go-to method in surveying, construction, and any field measurement where dropping a perpendicular height onto a base is impractical. The calculator also reports the perimeter — the simple sum of the three sides.
Enter side a, side b and side c to get the triangle's area and perimeter instantly — the sides can be in any matching unit.
Heron's formula first builds the semi-perimeter s — half the sum of the sides — then takes a square root of a product involving s and each side.
Area = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2Take a triangle with sides a = 3, b = 4 and c = 5. The semi-perimeter is s = (3 + 4 + 5) ÷ 2 = 6. Then the area is √(6 × (6 − 3) × (6 − 4) × (6 − 5)) = √(6 × 3 × 2 × 1) = √36 = 6 square units, and the perimeter is 3 + 4 + 5 = 12 units. Because 3-4-5 is a right triangle, you can check it against ½ × base × height = ½ × 3 × 4 = 6 — the same answer, confirming the formula.
The formula is exact for any genuine triangle, but a couple of points are worth keeping in mind.
Valid triangles and consistent units
The three sides must satisfy the triangle inequality — the longest side has to be shorter than the sum of the other two — or no triangle exists and the calculator returns nothing. Keep all three sides in the same unit; the perimeter comes back in that unit and the area in that unit squared. Heron's formula gives a plane (flat) triangle's area only — it does not apply to triangles drawn on a curved surface such as a globe.