Heron’s Formula Calculator

What this calculator does

Heron’s formula is a direct way to calculate triangle area from three side lengths without first knowing a height.

What Heron’s formula calculates

Heron’s formula calculates triangle area from three side lengths. It is useful when you do not know the height of the triangle.

A = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) / 2.

Step-by-step Heron example

For a triangle with sides 7, 8, and 9:

1. Calculate semiperimeter: s = (7 + 8 + 9) / 2 = 12.
2. Substitute into Heron’s formula: A = √(12 × 5 × 4 × 3).
3. Calculate the product: 12 × 5 × 4 × 3 = 720.
4. Take the square root: A ≈ 26.83 square units.

When not to use Heron’s formula

If you already know a base and perpendicular height, A = 1/2 × base × height is simpler. If the three side lengths do not form a valid triangle, Heron’s formula will not describe a real triangle area.

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