Centroid Calculator
Find the geometric center (centroid) of a set of 2D points with this free online centroid calculator. Enter x,y coordinates separated by semicolons to compute the average point of your data set instantly.
About This Calculator
This free online centroid calculator computes the geometric center (average point) of any set of 2D coordinates. Enter points in x,y format separated by semicolons, and the tool instantly calculates both the centroid x-coordinate (x̄) and centroid y-coordinate (ȳ) using the arithmetic mean formula. Perfect for students, engineers, and professionals working with coordinate geometry, statistics, or spatial data analysis.
Frequently Asked Questions
What is a centroid?
A centroid is the geometric center of a set of points in 2D space. It is computed by averaging the x-coordinates and y-coordinates of all points separately, giving the point (x̄, ȳ) that represents the mean location of the entire set.
How do I use this centroid calculator?
Enter your 2D points in the format x,y with each point separated by a semicolon. For example, 0,0; 2,0; 0,3 represents three points. The calculator will compute the average x and y coordinates to find the centroid of all entered points.
What is the formula for a centroid?
For a set of n points (x1,y1), (x2,y2), ..., (xₙ,yₙ), the centroid (x̄, ȳ) is calculated as x̄ = (x1 + x2 + ... + xₙ)/n and ȳ = (y1 + y2 + ... + yₙ)/n. This is simply the arithmetic mean of all x-coordinates and all y-coordinates.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration or hidden fees.
What is the difference between centroid and center of mass?
The centroid is purely a geometric property based on the average position of points, assuming uniform density. The center of mass accounts for mass distribution and can differ from the centroid when objects have non-uniform density. For a set of points with equal weight, they are the same.
Can I calculate centroid for 3D points?
This calculator handles 2D points (x,y). For 3D points, the same principle applies where you would also average the z-coordinates. A 3D centroid calculator extends the same averaging formula to include the third dimension.