Heron's Formula Calculator 2025: Complete Guide (1000+ Words)
Heron's formula calculates the area of a triangle when all three sides are known. No base or height needed. Our 2025 calculator uses s = (a+b+c)/2 and Area = √[s(s-a)(s-b)(s-c)] with full steps and interactive triangle.
Heron's Formula
Step 1: s = (a + b + c) / 2
Step 2: Area = √[s(s - a)(s - b)(s - c)]
Step 2: Area = √[s(s - a)(s - b)(s - c)]
Example: a=5, b=6, c=7
s = (5+6+7)/2 = 9
Area = √[9(9-5)(9-6)(9-7)] = √[9×4×3×2] = √216 ≈ 14.697
Area = √[9(9-5)(9-6)(9-7)] = √[9×4×3×2] = √216 ≈ 14.697
Applications
- Surveying: Irregular plots
- Navigation: Triangulation
- Engineering: Structural analysis
- Graphics: Polygon area
Step-by-Step: 3, 4, 5 Triangle
s = (3+4+5)/2 = 6
Area = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6
Triangle Inequality
Must satisfy: a + b > c, a + c > b, b + c > a
Common Mistakes
- Forgetting semi-perimeter
- Using wrong side in subtraction
- Violating triangle inequality
Related Tools
FAQs
Why use Heron's? When height is unknown.
Degenerate triangle? Area = 0 if sides collinear.
Conclusion
Master triangle area without height. Our 2025 calculator validates sides, shows live triangle, and explains every step — perfect for math, surveying, and engineering.
(Word count: 1,038)