Math
Square pyramid
Find volume, slant height and surface area of a right square pyramid.
Calculators / Math / Triangle circumcenter
Triangle circumcenter calculator
Find the centre of the circle passing through three non-collinear points.
On this page
Circumcenter x3
Circumcenter y3
Calculator controls
How to calculate
Find the centre of the circle passing through three non-collinear points.
Circumcenter x = ((x1^2+y1^2)*(y2-y3)+(x2^2+y2^2)*(y3-y1)+(x3^2+y3^2)*(y1-y2))/(2*(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))); Circumcenter y = ((x1^2+y1^2)*(x3-x2)+(x2^2+y2^2)*(x1-x3)+(x3^2+y3^2)*(x2-x1))/(2*(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2)))
Worked example
Vertex 1 x: 0; Vertex 1 y: 0; Vertex 2 x: 6; Vertex 2 y: 0; Vertex 3 x: 0; Vertex 3 y: 6.
Circumcenter x: 3 ; Circumcenter y: 3 .
Assumptions and limits
Use one Cartesian coordinate system. Collinear vertices have no finite circumcircle; nearly collinear points can amplify measurement and rounding errors.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the centre of the circle passing through three non-collinear points.
When this tool is useful
Circumcenter x = ((x1^2+y1^2)*(y2-y3)+(x2^2+y2^2)*(y3-y1)+(x3^2+y3^2)*(y1-y2))/(2*(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))); Circumcenter y = ((x1^2+y1^2)*(x3-x2)+(x2^2+y2^2)*(x1-x3)+(x3^2+y3^2)*(x2-x1))/(2*(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2)))
Understanding your inputs
| Input | What to enter |
|---|---|
| Vertex 1 x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vertex 1 y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vertex 2 x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vertex 2 y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vertex 3 x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vertex 3 y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Use one Cartesian coordinate system. Collinear vertices have no finite circumcircle; nearly collinear points can amplify measurement and rounding errors.
How is the result calculated?
Circumcenter x = ((x1^2+y1^2)*(y2-y3)+(x2^2+y2^2)*(y3-y1)+(x3^2+y3^2)*(y1-y2))/(2*(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2))); Circumcenter y = ((x1^2+y1^2)*(x3-x2)+(x2^2+y2^2)*(x1-x3)+(x3^2+y3^2)*(x2-x1))/(2*(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2)))