How does the Heron's Formula work?

Compute s = (a+b+c)/2 Then: Area = √(s·(s−a)·(s−b)·(s−c)) Then: Verify triangle inequality first Then: Result is exact for integer sides.

Can you give an example of how to use the Heron's Formula?

Example: Input a=3, b=4, c=5 gives a result of Area = 6 (right triangle).

Is the Heron's Formula free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Heron's Formula?

Our Heron's Formula uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Heron's Formula

Heron's Formula — Triangle Area

Side a

Side b

Side c

Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2

Heron's formula calculates triangle area from three side lengths. Named after Hero of Alexandria (c. 10–70 AD), it requires no height measurement.

Symbol	Name	Unit	Description
a, b, c	side lengths	length	—
s	semi-perimeter	length	—
A	triangle area	length²	—

Sides	Area
3,4,5	6
5,12,13	30
8,15,17	60
13,14,15	84

References

›Heron's formula — Wikipedia

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Heron's Formula

Heron's Formula — Triangle Area

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Classic Triangle Areas

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Heron's Formula — Triangle Area