Centroid Calculator — Geometric Centre of a Set of Points
Enter the coordinates of 2 to 4 points to find their centroid — the point at the arithmetic mean of all x and y values. It is the geometric balance point of the set.
Number of points
x-coordinate of the centroid — arithmetic mean of all x-coordinates
- 1
Sum of x-coordinates
0 + 6 + 3 = 9 - 2
Centroid x̄ = Σxᵢ ÷ n
9 ÷ 3 = 3
How does this calculator work?
The centroid of n points is x̄ = Σxᵢ/n, ȳ = Σyᵢ/n — the arithmetic mean of all coordinates. It is the balance point that minimises total squared distance. Enter 2–4 coordinate pairs to compute and visualise the centroid on a scatter plot.
Formula
How this is calculated
The centroid of a finite set of points is the arithmetic mean of their coordinates. For n points each with coordinates (xᵢ, yᵢ), sum all x-coordinates and divide by n to get x̄; do the same for y to get ȳ. The centroid (x̄, ȳ) minimises the sum of squared distances to all input points — making it the natural balance point of the set.
In physics, the centroid of a collection of equal-mass particles coincides with the centre of mass of the system. In geometry, the centroid of a triangle's three vertices is the point where all three medians intersect (one-third of the way from each side to its opposite vertex). For engineering and computer graphics, centroids are used to position, rotate and scale shapes, define local coordinate origins, and measure how far a region is from an axis.
This calculator handles 2, 3 or 4 equally-weighted points in the Cartesian plane. Coordinates can be any real numbers. The scatter plot marks the input points and the centroid (G, in red) so you can verify it lies within the cluster of input points.
Frequently asked questions
The centroid is the point at the geometric centre of the set. If you placed equal-weight masses at each input point, the centroid is where a pin would perfectly balance the whole system. On the Cartesian plane it is simply (mean x, mean y).
For a set of equal-mass points, yes — the centroid and the centre of mass coincide. If the points have different masses, you need a weighted average: x̄ = Σ(wᵢ xᵢ) / Σwᵢ. This calculator assumes equal weights.
Yes. The centroid of a set of points always lies inside or on the boundary of the convex hull (the smallest convex polygon that encloses all the points). For a triangle this means the centroid is strictly inside the triangle.
Also known as
TG we-Calculate Editorial Team. (2026). Centroid Calculator — Geometric Centre of a Set of Points [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/centroid-calculator
TG we-Calculate Editorial Team. "Centroid Calculator — Geometric Centre of a Set of Points." TG we-Calculate. 2026. https://we-calculate.com/calculator/centroid-calculator.
TG we-Calculate Editorial Team, "Centroid Calculator — Geometric Centre of a Set of Points," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/centroid-calculator
@misc{wecalculate_centroid_calculator, title = {Centroid Calculator — Geometric Centre of a Set of Points}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/centroid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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