Area of Circle Within a Triangle

The Area of Circle Within a Triangle calculator computes the area (blue circle in diagram) of circle that is perfectly inscribed within a triangle.

INSTRUCTIONS: Choose units and enter the following:

• (a) Length of Side a
• (b) Length of Side b
• (c) Length of Side c

Area of Circle Within a Triangle (A): The area is returned in square meters and the radius (r) is returned in meters.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for  Area of Circle Within a Triangle equation is:

`A = pi * (sqrt((a+b+c)/2((a+b+c)/2-a)((a+b+c)/2-b)((a+b+c)/2-c))  / ((a+b+c)/2))^2`

where:

• A = Area of Circle inscribe within a triangle.
• a = length of side a
• b = length of side b
• c = length of side c

Note: (a+b+c)/2 is the semi-perimeter of the triangle

A triangle is a polygon with three sides, three vertices (corners), and three angles. Triangles can be classified based on the lengths of their sides and the measures of their angles as follows:

By Side Lengths:

• Equilateral Triangle: All three sides are equal in length.
• Isosceles Triangle: Two sides are equal in length.
• Scalene Triangle: All three sides have different lengths.

By Angle Measures:

• Acute Triangle: All three angles are less than 90 degrees.
• Right Triangle: One angle is exactly 90 degrees.
• Obtuse Triangle: One angle is greater than 90 degrees.

The sum of the interior angles of any triangle always adds up to 180 degrees. 

Triangle Calculators

• Area of Triangle (base and height)
• Area of Triangle (two sides and interior angle)
• Area of Triangle (two angles and interior side)
• Area of Triangle (three sides)
• Area of Equilateral Triangle
• Area of Triangle (three points)
• Height of Triangle
• Width of Triangle
• Triangle Perimeter
• Interior Angle of a triangle based on the length of three sides
• Semi-perimeter of a triangle
• Area of Circle Within a Triangle
• Area of Circle Around a Triangle
• Area between two vectors
• Triangle Volume