Math

Orthocenter Calculator

Find the orthocenter of a triangle from its three vertices.

Aₓ

A_y

Bₓ

B_y

Cₓ

C_y

Calculated Output

Orthocenter x 2

Orthocenter y 1.6

Formula: Intersection of two altitudes

Step-by-Step Breakdown

1. Values used:

2. Aₓ = 0

3. A_y = 0

4. Bₓ = 6

5. B_y = 0

6. Cₓ = 2

7. C_y = 5

9. Orthocenter x = 2

10. Orthocenter y = 1.6

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The math behind it

Each altitude passes through a vertex and is perpendicular to the opposite side. Intersecting any two altitudes gives the orthocenter.

For a right triangle, the orthocenter sits exactly at the right-angle vertex.

Can it lie outside the triangle?

Yes — for an obtuse triangle the orthocenter is outside it.