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Geometry

Triangle Orthocenter Calculator

Find the intersection of the altitudes for three planar vertices.

Use consistent dimensionsArea and volume units explained below
Geometry desk
Geometry desk

Match each dimension to the shape and keep units consistent.

See the method

Set the dimensions

Runs on your device

Your measurement

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter vertex a x, vertex a y, vertex b x, vertex b y, vertex c x, vertex c y.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Translate A to the origin, solve for circumcenter U, then orthocenter H=A+B+C−2U in absolute coordinates.

A WORKED EXAMPLE

Using vertex a x = 0, vertex a y = 0, vertex b x = 4, vertex b y = 0, vertex c x = 1, vertex c y = 3, the result is (1, 1). Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Planar non-degenerate triangle. The orthocenter can be outside an obtuse triangle and is the right-angle vertex of a right triangle.

What to keep in mind

Planar non-degenerate triangle. The orthocenter can be outside an obtuse triangle and is the right-angle vertex of a right triangle. Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.

Common questions

How do I use this triangle orthocenter calculator?

Find the intersection of the altitudes for three planar vertices. Enter vertex a x, vertex a y, vertex b x, vertex b y, vertex c x, vertex c y. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Planar non-degenerate triangle. The orthocenter can be outside an obtuse triangle and is the right-angle vertex of a right triangle.

Methodology maintained by ClarityKit. How these tools are built and checked.