Heron's Formula Calculator
Enter three side lengths to calculate triangle area using Heron's formula.
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Request a ToolHow to Use Heron's Formula Calculator
This calculator finds the area of any triangle when you know all three side lengths.
- Enter sides a, b, and c. Type the three side lengths of your triangle.
- Read the area. The calculator uses Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2.
- Check validity. If the three sides cannot form a triangle, no result is shown.
About Heron's Formula
Heron's formula, attributed to Heron of Alexandria (circa 60 AD), calculates the area of a triangle from its three side lengths without needing height or angles. The semi-perimeter s = (a+b+c)/2 is computed first, then Area = sqrt(s(s-a)(s-b)(s-c)). The formula works for any valid triangle. A valid triangle requires that each side be less than the sum of the other two sides (triangle inequality).
Frequently Asked Questions
What is Heron's formula?
Heron's formula calculates triangle area from three sides: Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2.
When should I use Heron's formula?
Use it when you know all three side lengths but not the height. If you have base and height, use Area = 0.5 * base * height instead.
What is the triangle inequality?
The triangle inequality states that each side must be less than the sum of the other two: a < b + c, b < a + c, and c < a + b.