ClarityHow to use this tool
- Enter vertex a x, vertex a y, vertex b x, vertex b y, vertex c x, vertex c y.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
Translate A to the origin and solve the perpendicular-bisector equations 2u·AB=|AB|² and 2u·AC=|AC|². Translate the center back; its distance to A is the radius.
Using vertex a x = 0, vertex a y = 0, vertex b x = 4, vertex b y = 0, vertex c x = 0, vertex c y = 3, the result is 2.5. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
Yes. An obtuse triangle has its circumcenter outside; a right triangle has it at the midpoint of the hypotenuse.
What to keep in mind
Main result is radius. Nearly collinear points are numerically sensitive; coordinates must share one unit. Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.
Common questions
Can the center lie outside the triangle?
Yes. An obtuse triangle has its circumcenter outside; a right triangle has it at the midpoint of the hypotenuse.
How can I check the result?
Translate A to the origin and solve the perpendicular-bisector equations 2u·AB=|AB|² and 2u·AC=|AC|². Translate the center back; its distance to A is the radius. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.