Enter the area and semi-perimeter of the triangle into the calculator to determine the inradius. This calculator can also evaluate any of the variables given the others are known.

Inradius Formula

The following formula is used to calculate the inradius of a triangle.

r = A / s

Variables:

  • r is the inradius of the triangle (units) A is the area of the triangle (square units) s is the semi-perimeter of the triangle (units)

To calculate the inradius of a triangle, first calculate the area of the triangle and the semi-perimeter. The semi-perimeter is half the sum of the lengths of the triangle’s sides. Then, divide the area by the semi-perimeter to get the inradius.

What is an Inradius?

An inradius refers to the radius of the inscribed circle of a geometric figure, most commonly a triangle. The inscribed circle, or incircle, is the largest possible circle that can be drawn within the figure, touching all its sides but not crossing them. The inradius is the distance from the center of this circle to any point on its circumference. In a triangle, the inradius can be found using the area and the semiperimeter of the triangle.

How to Calculate Inradius?

The following steps outline how to calculate the Inradius of a triangle.


  1. First, determine the area of the triangle (A) in square units.
  2. Next, determine the semi-perimeter of the triangle (s) in units.
  3. Next, gather the formula from above: r = A / s.
  4. Finally, calculate the inradius (r) of the triangle.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Area of the triangle (A) = 36 square units

Semi-perimeter of the triangle (s) = 15 units