\[\begin{aligned}
r &= \frac{A}{s} \\
s &= \frac{a+b+c}{2}
\end{aligned}\]
Variables
rtriangle inradius
Atriangle area
ssemi-perimeter
aside length a
bside length b
cside length c
Description
What is this formula?
The triangle inradius formula calculates the radius of the inscribed circle of a triangle. The inscribed circle touches all three sides internally, and its center is called the incenter.
When to use it
Use this formula when the triangle area and side lengths are known and the radius of the inscribed circle must be determined.
Example
For a triangle with:
a = 5
b = 6
c = 7
A = 14.7
First calculate the semi-perimeter:
s = (5+6+7)/2 = 9
Then:
r = 14.7/9
r ≈ 1.63
Applications
Used in geometry, engineering, architecture, CAD systems, and geometric optimization problems involving inscribed circles.