Math
Triangle circumcenter
Find the centre of the circle passing through three non-collinear points.
Calculators / Math / Triangle orthocenter
Triangle orthocenter calculator
Locate the intersection of the three triangle altitudes from vertex coordinates.
On this page
Orthocenter x0
Orthocenter y0
Calculator controls
How to calculate
Locate the intersection of the three triangle altitudes from vertex coordinates.
Orthocenter x =
x1+x2+x3-2*(((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))))Orthocenter y =
y1+y2+y3-2*(((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
- Orthocenter x: 0
- Orthocenter y: 0
Assumptions and limits
Use one Cartesian coordinate system. Collinear vertices are rejected; nearly collinear coordinates may amplify rounding errors.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Locate the intersection of the three triangle altitudes from vertex coordinates. The orthocenter can lie outside an obtuse triangle. Its location is not necessarily the centre of the shape.
When this tool is useful
The orthocenter can lie outside an obtuse triangle. Its location is not necessarily the centre of the shape.
Understanding your inputs
| Input | Example |
|---|---|
Vertex 1 x x1 | 0 |
Vertex 1 y y1 | 0 |
Vertex 2 x x2 | 6 |
Vertex 2 y y2 | 0 |
Vertex 3 x x3 | 0 |
Vertex 3 y y3 | 6 |
Frequently asked questions
Which assumptions matter for this result?
Use one Cartesian coordinate system. Collinear vertices are rejected; nearly collinear coordinates may amplify rounding errors.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.