Triangle Circumradius
Triangle Circumradius
\[R = \frac{abc}{4A}\]
Variables
R = triangle circumradius
A = triangle area
a = side length a
b = side length b
c = side length c
Description
What is this formula?
The triangle circumradius formula calculates the radius of the circumscribed circle around a triangle. This circle passes through all three vertices of the triangle, and its center is called the circumcenter.
When to use it
Use this formula when the side lengths and area of a triangle are known and the radius of the circumcircle must be calculated.
Example
For a triangle with:
a = 5
b = 6
c = 7
A = 14.7
Then:
R = (5×6×7)/(4×14.7)
R ≈ 3.57
Applications
Used in geometry, trigonometry, engineering design, CAD systems, surveying, and computational geometry.
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