Heron's Formula Calculator

Area
Semi-Perimeter (s)
Valid Triangle?

How It Works

This heron's formula calculator uses established formulas to provide accurate results.

The basic rule:

  • s = (a + b + c) / 2
  • A = √[s(s-a)(s-b)(s-c)]
  • Perimeter = a + b + c

Results are estimates. Consult a professional for critical decisions.

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Frequently Asked Questions

What is Heron's formula?

Heron's formula calculates the area of a triangle given only its three side lengths. First find the semi-perimeter s = (a+b+c)/2, then the area = √[s(s-a)(s-b)(s-c)].

Who was Heron of Alexandria?

Heron (or Hero) was a Greek mathematician and engineer from the 1st century AD in Alexandria, Egypt. He is credited with this formula, though it may have been known earlier by Archimedes.

When should I use Heron's formula instead of ½bh?

Use Heron's formula when you know all three sides but do not know the height. If you know the base and height, the standard formula A = ½bh is simpler.

Can Heron's formula give a negative value under the square root?

Yes, if the three lengths do not form a valid triangle (violating the triangle inequality), the expression under the square root will be negative, indicating no valid triangle exists.