Finds the geometric center of a triangle — the point where all three medians intersect — from its three corner coordinates.
How it works
The x-coordinates of all three vertices are averaged, and the y-coordinates are averaged separately, giving the centroid’s coordinates.
What this does not include
This does not include weighting by mass — for a mass-weighted balance point instead of a plain geometric average, use this site’s center of mass calculator instead.
How to use this calculator
- Enter the x and y coordinates of all three vertices.
A worked example
Triangle vertices (0,0), (4,0), (2,6): centroid = average of the three x-values and three y-values = (2, 2).
Vertices (1,1), (5,1), (3,7): centroid = (3, 3).
What the variables mean
| Variable | Meaning |
|---|---|
| (x1,y1), (x2,y2), (x3,y3) | The triangle’s three vertex coordinates |
Edge cases worth knowing
The centroid is simply the average of the three vertices — average all the x-coordinates, average all the y-coordinates, independently, the same averaging principle behind this site’s midpoint calculator.
The centroid is the triangle’s balance point — if cut from a rigid, uniform material, the triangle would balance perfectly on a pin placed at this point.
Frequently asked questions
What is a median, in this context?
A line segment from one vertex to the midpoint of the opposite side — a triangle has three medians, and they always meet at the centroid.
Does the centroid always lie inside the triangle?
Yes — unlike some other triangle centers, the centroid always falls within the triangle’s interior, regardless of its shape.
Is the centroid the same as the triangle’s “center of gravity”?
Yes, for a triangle of uniform density — the centroid corresponds to where a physical triangular plate would balance perfectly.
