How to Calculate Heron's Formula
What is Heron's Formula?
Heron's formula calculates triangle area from three side lengths. Named after Hero of Alexandria (c. 10–70 AD), it requires no height measurement.
Formula
s = (a+b+c)/2; A = √(s(s−a)(s−b)(s−c))
- a, b, c
- side lengths (length)
- s
- semi-perimeter (length)
- A
- triangle area (length²)
Step-by-Step Guide
- 1Compute s = (a+b+c)/2
- 2Area = √(s·(s−a)·(s−b)·(s−c))
- 3Verify triangle inequality first
- 4Result is exact for integer sides
Worked Examples
Input
a=3, b=4, c=5
Result
Area = 6 (right triangle)
Input
a=13, b=14, c=15
Result
Area = 84
Frequently Asked Questions
What is the difference between heron-formula and heron-formula-calc?
The -calc version is a focused calculator; heron-formula is the broader educational reference.
Can Heron's formula be used for any triangle?
Yes, any valid triangle (satisfying triangle inequality). It works for right, acute, and obtuse triangles.
How does Heron's formula compare to ½ × base × height?
Both give the same area. Heron's formula is used when height is unknown; base × height when height is known.
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