Heron's Formula Calculator
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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Explore Allday Everyday Math →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.