Orthocenter Calculator

Category: Geometry

- November 17, 2025

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Calculate and visualise the orthocenter of a triangle. The orthocenter is the point where all three altitudes of a triangle intersect. This calculator helps understand the geometric properties of triangles and their orthocenter.

Triangle Coordinates

Point A (x):

Point A (y):

Point B (x):

Point B (y):

Point C (x):

Point C (y):

Display Options

Decimal Places:

Show calculations

Show all altitudes

About the Orthocenter

The orthocenter is the point where all three altitudes of a triangle intersect. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side.

Properties of the Orthocenter

Location: The orthocenter can be inside, outside, or on the triangle, depending on the triangle type.
For acute triangles: The orthocenter is inside the triangle.
For right triangles: The orthocenter is at the vertex with the right angle.
For obtuse triangles: The orthocenter is outside the triangle, opposite to the obtuse angle.
Equilateral triangles: The orthocenter coincides with the incenter, centroid, and circumcenter.

Mathematical Calculation

To find the orthocenter:

Find the equations of two altitudes of the triangle
Solve these equations to find their intersection point
The third altitude will also pass through this point

Alternatively, we can use coordinate geometry formulas to directly calculate the orthocenter.

Applications

The concept of the orthocenter is used in:

Geometric design and construction
Engineering and physics for calculating centres of structures
Computer graphics for shape manipulation
Navigation and triangulation methods

What Is an Orthocenter?

The orthocenter is a special point in a triangle. It's where all three altitudes meet. An altitude is a line from a triangle's corner that goes straight down to the opposite side. Understanding where this point is helps us learn more about triangles and their properties.

How the Orthocenter Calculator Works

The Orthocenter Calculator makes it easy to find and display the orthocenter of a triangle. You simply enter the coordinates of the three corners, or vertices, of the triangle. The calculator does the Math to find the orthocenter and also shows you a visual representation. This way, you can quickly see where the altitudes intersect.

Inputting Triangle Coordinates

Enter the x and y values for Point A, B, and C.
Point A can start at (0,0), Point B at (6,0), and Point C can be set at (3,5).
These points represent the vertices of your triangle!

Understanding Display Options

The calculator offers options to customise how results are shown. You can choose how many decimal places to display, from none to four. Additionally, you can decide whether to see the calculations and the lengths of the altitudes. This is great for learning and checking your understanding of the topic.

Results You Can Expect

Once the calculations are done, you’ll see the orthocenter's coordinates displayed. You’ll also get the lengths of the altitudes from each vertex to the opposite side. This information helps you understand the shape and size of the triangle better, making it useful for studies or projects.

Visual Learning with Triangle Representation

The calculator includes a feature that visualizes the triangle on a canvas. You can see the triangle along with its altitudes and the orthocenter marked. This visual aid is helpful for grasping the concepts related to the orthocenter and its position in different types of triangles.

Why the Orthocenter Matters

It's key in understanding different triangle types, like acute, right, and obtuse.
It plays a role in various fields like engineering and computer graphics.
Knowing the orthocenter helps in solving real-world problems involving shapes and structures.

Learning More About Triangles

Using the Orthocenter Calculator is a fun way to learn. Besides just finding the orthocenter, you can explore triangle properties and calculations. This tool is perfect for students, teachers, or anyone interested in Geometry. You’ll gain a deeper understanding of triangles, making your math studies easier and more engaging.