What is the orthocenter of a triangle?

The orthocenter is the point where the three altitudes of a triangle intersect. Each altitude is a line segment from a vertex perpendicular to the opposite side (or its extension).

Where does the orthocenter lie relative to the triangle?

For an acute triangle the orthocenter is inside the triangle. For a right triangle it coincides with the right-angle vertex. For an obtuse triangle it falls outside the triangle, beyond the obtuse vertex.

What if the three points are collinear?

Collinear points do not form a triangle, so no orthocenter exists. The calculator detects this and displays an error instead of producing a result.

How is the orthocenter different from the centroid or circumcenter?

The centroid is the average of the vertices (center of mass). The circumcenter is equidistant from all three vertices (circumscribed circle center). The orthocenter is the altitude intersection. All three are collinear on the Euler line for non-equilateral triangles.

Do all three altitudes really meet at one point?

Yes — this is a classical theorem in Euclidean geometry. The calculator confirms it by computing from two altitudes and verifying the result lies on the third.

Triangle Orthocenter Calculator

Name: Triangle Orthocenter Calculator
Availability: InStock
Author: Nham Vu

Enter three vertex coordinates to find the orthocenter — the point where all three altitudes of a triangle meet.

Vertex Coordinates

Vertex A

Vertex B

Vertex C

Quick Presets

Enter vertex coordinates and click Calculate

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Summary

Enter three vertex coordinates to find the orthocenter — the point where all three altitudes of a triangle meet.

How it works

Enter the x and y coordinates for each of the three triangle vertices.
The calculator finds the altitude from each vertex (a line through the vertex, perpendicular to the opposite side).
It then solves the system formed by two altitudes to find their intersection point.
That intersection is the orthocenter — verified to lie on all three altitudes.
Results include the orthocenter coordinates and a visual diagram.

Use cases

Solving triangle geometry problems in high-school or university coursework.
Verifying hand-calculated orthocenter coordinates against a known answer.
Exploring the orthocentric system in computational or projective geometry.
CAD or game-development work that requires altitude intersection on a mesh face.
Understanding how orthocenter position changes with triangle type (acute vs. obtuse).

Frequently Asked Questions

Last updated: 2026-07-26 · Reviewed by Nham Vu