Enter the three vertices (x, y) and click Calculate Circumcircle.

The circumcircle of a triangle is the unique circle that passes through all three vertices of the triangle. Its center is called the circumcenter, and its radius is called the circumradius. The circumcenter is the intersection point of the perpendicular bisectors of the triangle's sides. For any non-degenerate triangle (points not collinear), exactly one circumcircle exists. The circumradius R can be calculated using the formula R = (a·b·c)/(4·K), where a, b, c are the side lengths and K is the area of the triangle. Alternatively, using coordinates, the circumcenter is found by solving the perpendicular bisector equations. The circumcircle is fundamental in geometry, trigonometry, and engineering applications such as triangulation, navigation, and computer graphics. This calculator computes the circumcenter and circumradius from the three vertices and displays the results with additional triangle properties.

1. Enter the x and y coordinates of Vertex A.
2. Enter the x and y coordinates of Vertex B.
3. Enter the x and y coordinates of Vertex C.
4. Click Calculate Circumcircle to compute the circumcenter and circumradius.
5. The result shows the circumcenter, circumradius, area, side lengths, and inradius.
6. Click Reset to restore default example values.