Incircle Radius Calculator
Enter the three side lengths of any triangle. The Incircle Radius Calculator instantly computes the radius of the inscribed circle (r = A/s).
About the Incircle Radius Calculator
The Incircle Radius Calculator is a precise, scientifically validated tool that computes the radius of the unique circle tangent to all three sides of any triangle (the incircle). This Incircle Radius Calculator uses the universally accepted formula \( r = \frac{A}{s} \), where \( A \) is the area (computed via Heron’s formula) and \( s \) is the semi-perimeter. Proudly supported by Agri Care Hub.
Scientific Formula
where s = (a+b+c)/2 and A = √[s(s−a)(s−b)(s−c)] (Heron’s formula)
Why the Incircle Radius Calculator Is Important
Every triangle has exactly one incircle — a fundamental theorem of Euclidean geometry. The inradius r is essential in architecture (vault design), engineering (pipe and cable routing), computer graphics (medial axis), and pure mathematics (triangle centers, area relations). It is directly related to the incenter — the intersection point of the angle bisectors and the center of the incircle.
User Guidelines
- Enter the three side lengths of any triangle (in any units).
- Click “Calculate Incircle Radius”.
- The calculator instantly returns: • Inradius r • Area of the triangle • Semi-perimeter • Step-by-step calculation using Heron’s formula
When Should You Use This Calculator?
- High-school and college geometry homework
- Preparing for SAT, ACT, GCSE, IB, or math competitions
- Architecture and interior design (tangent circle problems)
- Engineering and manufacturing (clearance calculations)
- Teaching triangle centers and incircle properties
- Computer graphics and computational geometry
Scientific Foundation
The formula \( r = \frac{A}{s} \) was known to Archimedes and rigorously proven using the properties of tangents from a point to a circle. It holds for all triangles — acute, right, and obtuse. For full mathematical treatment, see the Wikipedia article on Incircle Radius.
Special Cases
• Equilateral triangle: r = side × √3 / 6
• Right triangle: r = (a + b − c)/2 where c is hypotenuse
• The calculator handles all cases automatically.
Limitations
The calculator assumes a valid triangle (triangle inequality satisfied). It works in Euclidean plane geometry only.
Conclusion
The Incircle Radius Calculator brings one of the most elegant theorems in mathematics into an instant, accurate tool. Whether you’re a student exploring triangle properties, a teacher demonstrating the incenter, or a professional working with tangent geometry, this calculator delivers mathematically perfect results every time. For more educational tools, visit Agri Care Hub.