What is the centroid of a triangle?

The centroid is the point where the three medians of a triangle meet. A median connects a vertex to the midpoint of the opposite side. The centroid always lies inside the triangle and divides each median in a 2:1 ratio from vertex to midpoint.

What formula is used to calculate the centroid?

The centroid coordinates are the arithmetic mean of the vertex coordinates: x_c = (x1 + x2 + x3) / 3 and y_c = (y1 + y2 + y3) / 3.

Can the centroid be outside the triangle?

No. The centroid always lies inside the triangle, regardless of whether the triangle is acute, right, or obtuse. This distinguishes it from other triangle centers like the orthocenter or circumcenter.

Can I use negative or decimal coordinates?

Yes. The calculator accepts any real numbers for vertex coordinates, including negative values and decimals.

What happens if the three points are collinear?

Collinear points do not form a triangle — they lie on a single line. The tool will detect this and show an error rather than computing a degenerate centroid.

Triangle Centroid Calculator

Enter the (x, y) coordinates of three triangle vertices to find the centroid and see a labeled diagram.

Vertex Coordinates

A Vertex A

x₁

y₁

B Vertex B

x₂

y₂

C Vertex C

x₃

y₃

Diagram

Triangle (blue), medians (dashed), centroid G (red dot)

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Summary

The centroid of a triangle is the point where its three medians intersect. It is the arithmetic mean of the three vertex coordinates: x_c = (x1 + x2 + x3) / 3 and y_c = (y1 + y2 + y3) / 3. This tool computes that point instantly and draws the triangle, its medians, and the centroid on an interactive diagram.

How it works

Enter the x and y coordinates for each of the three triangle vertices (A, B, C).
The centroid is computed as the average: x_c = (x1+x2+x3)/3, y_c = (y1+y2+y3)/3.
The result panel displays the centroid coordinates rounded to 4 decimal places.
The canvas draws the triangle, all three medians, and marks the centroid.
Change any coordinate value to instantly update both the result and the diagram.

Use cases

Find the balance point (center of mass) of a triangular plate.
Locate the centroid for structural engineering and load distribution problems.
Verify hand-calculated centroid coordinates in geometry homework.
Explore how the centroid shifts as triangle vertices are moved.
Compute centroids for computational geometry and mesh algorithms.
Teach the median-intersection property of triangle centroids visually.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu