Triangle Inradius Calculator

About this calculator

Every triangle has a unique inscribed circle — the largest circle that fits inside it, tangent to all three sides — and its radius follows from a simple ratio: r = Area / s, where s is the semiperimeter, s = (a + b + c) / 2. The area itself is typically found first via Heron's formula, Area = √(s(s−a)(s−b)(s−c)), from the three side lengths alone.

This relationship connects a triangle's size directly to the radius of the circle that can be cut from its interior, which is why machinists and metalworkers use it when fitting the largest circular disk or fillet inside a triangular piece of stock, and why it appears in triangulation-based centroid calculations in computational geometry and CAD software.

Geometry students proving the r = Area/s relationship, engineers and designers working with triangular cross-sections, and puzzle or game designers computing inscribed shapes all rely on this formula because it links three measurable side lengths directly to an otherwise hard-to-measure interior radius.