Heron's Formula Calculator - Area from 3 Sides - Interactive Online Tool

About Heron's Formula

Heron's formula is a mathematical formula for calculating the area of a triangle when you know the lengths of all three sides. It was first described by Hero of Alexandria in the 1st century AD.

The Formula:

Area = √[s(s-a)(s-b)(s-c)]

where s = (a+b+c)/2 is the semi-perimeter

When to Use Heron's Formula:

• When you know all three side lengths of a triangle
• When you don't know the height of the triangle
• For any type of triangle (scalene, isosceles, equilateral)
• When other area formulas are not applicable

Step-by-Step Process:

1. Verify triangle inequality: Check that a+b>c, a+c>b, and b+c>a
2. Calculate semi-perimeter: s = (a+b+c)/2
3. Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)]
4. Calculate the result: Evaluate the square root

Applications:

• Land surveying and property measurement
• Construction and architectural planning
• Engineering design calculations
• Navigation and GPS systems
• Computer graphics and 3D modeling

Advantages:

• Works for any triangle type
• Only requires side lengths (no angles or heights)
• Provides exact results
• Historically significant and widely recognized

Historical Note:

Named after Hero of Alexandria (c. 10-70 AD), though the formula may have been known earlier. Hero was a Greek mathematician and engineer who made significant contributions to geometry and mechanics.