Triangle medians & the centroid
The centroid of a triangle is the average of its vertices: G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3). It is where the three medians meet, and it divides each median in a 2:1 ratio from the vertex.
Triangle medians & the centroid calculator
Find the balance point of a triangle. Change a value and the diagram, result, and working update together.
Your measurements
Drag a vertex or enter coordinates. Use the challenges to discover how shapes behave.
Discovery challenges
Choose a goal, then move the vertices to find a solution. Classification uses a small numerical tolerance.
Why it works
The idea
A median joins a vertex to the midpoint of the opposite side. All three medians meet at the centroid G, which lies inside every non-degenerate triangle. The centroid divides each median in a 2:1 ratio, with the longer part next to the vertex.
Work through an example
1Work through an example
- For A(−4, −3), B(4, −3), and C(0, 4), the centroid is (0, −2/3). The base AB has length 8 and the height from C is 7, so the area is 28 square units. Moving C horizontally while keeping its height preserves that area.
Common mistakes
- A median is not necessarily perpendicular to its opposite side. The centroid, circumcenter, incenter, and orthocenter are different points in general; they coincide in an equilateral triangle.
Make the formula move.
Open the full tool for a larger workspace.