Calculators

Triangle Centroid Calculator

Find the centroid of a triangle from three Cartesian vertices locally in your browser, with signed coordinates and copyable results.

Enter the three vertices of a triangle in a flat Cartesian plane, using the same unit on both axes. The centroid is the average of the vertex coordinates. Signed decimals and scientific notation are accepted; use zero or coordinate magnitudes from 1e-100 to 1e100. Collinear or repeated vertices return their coordinate average. Calculations stay in your browser.

Find the intersection of a triangle’s medians.

For vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), the centroid is G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3). It is the center of mass of a uniform triangular lamina and divides each median in a 2:1 ratio measured from the vertex. For A = (0, 0), B = (6, 0), C = (0, 9), G = (2, 3). This is not generally the circumcenter or incenter. Collinear and repeated vertices still have a coordinate average, but do not define a nondegenerate triangle. Use consistent units on a flat Cartesian plane, not geographic latitude and longitude. Signed decimals and scientific notation are supported; coordinate magnitudes must be zero or 1e-100 to 1e100. Results use browser floating-point arithmetic and display up to 12 significant digits; small differences between very large coordinates may be lost. Inputs remain in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

How do I calculate the triangle centroid?

Average the three x coordinates and the three y coordinates separately. Vertices (0, 0), (6, 0), and (0, 9) have centroid (2, 3).

How does the centroid divide a median?

In a nondegenerate triangle, each median joins a vertex to the midpoint of the opposite side. The centroid lies two thirds of the way along that median from the vertex.

Are collinear or repeated vertices accepted?

Yes. The calculator returns the coordinate average, even though these points do not form a nondegenerate triangle.

Is this the same as the circumcenter?

Not generally. The centroid is the intersection of the medians. The circumcenter is the intersection of the perpendicular bisectors.

What inputs and precision are supported?

Use signed decimal coordinates or scientific notation with magnitudes zero or 1e-100 to 1e100. Results show up to 12 significant digits. Use consistent Cartesian units rather than latitude and longitude.

Are coordinates sent to a server?

No. All calculations happen locally in your browser.