⭕ Inscribed Circle Calculator

Calculate the inscribed circle radius and area of a triangle.

Side a Side b Side c

What is the Inscribed Circle?

The circle tangent to all three sides of a triangle. Its center (incenter, I) is the intersection of the three angle bisectors.

r = S / s

S는 삼각형 넓이, s는 반둘레(perimeter/2)입니다.

s = (a + b + c) / 2

S = √(s(s−a)(s−b)(s−c))

r = (a + b − c) / 2 × tan(C/2)

This formula shows that for a right triangle (C=90°), r = (a + b − c) / 2.

S = r × s

The product of the inradius and the semi-perimeter equals the triangle area.

I = (a·A + b·B + c·C) / (a + b + c)

The incenter is the weighted average of the vertices, with each side length as the weight.