Find where a triangle's three altitudes meet — with the triangle type and inside/outside position.
The orthocenter is where the triangle's three altitudes meet. For a right triangle it is the right-angle vertex; for an obtuse triangle it falls outside the triangle — the calculator says which case yours is.
Orthocenter
How to use this tool
Three (x, y) pairs — any order, any scale.
The big result is the (x, y) point where the altitudes meet.
Acute, right or obtuse determines where the point falls.
The centroid is the average of the vertices; the orthocenter is the altitudes' meeting point.
Formula & worked example
For the triangle (0, 0), (4, 0), (2, 3): the altitude from (2, 3) is the vertical line x = 2, and the altitude from (0, 0) has slope 2/3, meeting at (2, 4/3) ≈ (2, 1.3333). The triangle is acute, so the orthocenter lies inside it.
Limitations — read this before you rely on it
Requires three non-collinear points; collinear points give no triangle and no orthocenter. Results are coordinate geometry for a flat plane — they do not apply to triangles on a sphere. Very flat triangles can give rounding-sensitive coordinates.
Frequently asked questions
The point where the triangle's three altitudes meet. An altitude runs from a vertex perpendicular to the opposite side.
Draw (or compute) two altitudes and find their intersection — the third altitude passes through the same point. This calculator computes it from the three vertices.
No. The centroid is the average of the three vertices (the triangle's balance point); the orthocenter is where the altitudes meet. They coincide only in an equilateral triangle.
At the right-angle vertex, because the two legs are themselves altitudes.
Yes — for an obtuse triangle it falls outside, beyond the obtuse vertex. For an acute triangle it is inside.