Heron's Formula Calculator to Calculate Triangle Area from Three Sides

What is Heron's Formula?

Heron's Formula calculates the area of a triangle from just its three side lengths, without needing the height. Named after Hero of Alexandria (~60 AD), it uses an intermediate quantity called the semi-perimeter (s). It is especially useful in surveying, computer graphics, and when height is unknown.

📐 Heron's Formula Calculator

Free calculator for instant results.

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📐 Formula

Area = √[s(s−a)(s−b)(s−c)]

s = (a+b+c)/2 (semi-perimeter). Requires triangle inequality: each side < sum of other two.

📝 Worked Example

Triangle with sides a=5, b=6, c=7:
s = (5+6+7)/2 = 9
Area = √[9×4×3×2] = √216 = 14.70 square units

📝 How to Use

Enter Side aFirst side length in any unit.

Enter Side bSecond side length (same unit).

Enter Side cThird side length.

CalculateView area, perimeter, semi-perimeter, and triangle type (scalene/isosceles/equilateral).

❓ FAQ

How do I know if three sides form a valid triangle?

The triangle inequality: each side must be less than the sum of the other two. If violated, no triangle exists and the formula gives an imaginary result.

Is Heron's formula numerically stable?

For very flat triangles (one very short side), subtracting near-equal numbers causes numerical errors. The Kahan stable version avoids this issue.

What is Heron's Formula?