While searching the web, solutions for finding centroids of polygons come up rather often. What I'm interested in is finding a centroid of a cluster of points. A weighted mean of sorts.

Can you provide some pointers, pseudo code (or even better, an R package that has already solved this) or links of how this issue can be tackled?

@iant has suggested a method to average coordinates and use that for the centroid. This is exactly what crossed my mind when I saw the right picture on this web page.

Here is some simple R code to draw the following figure that demonstrates this (× is the centroid):

xcor <- rchisq(10, 3, 2)
ycor <- runif(10, min = 1, max = 100)
mx <- mean(xcor)
my <- mean(ycor)

plot(xcor, ycor, pch = 1)
points(mx, my, pch = 3)

enter image description here

cluster::pam()$medoids returns a medoid of a set of cluster. This is an example from @Joris Meys:

df <- data.frame(X = rnorm(100, 0), Y = rpois(100, 2))
plot(df$X, df$Y)
points(pam(df, 1)$medoids, pch = 16, col = "red")

3 Answers 3


just average the X and Y coordinates (multiply by a weight if you want) and there is your centroid.


To calculate the centroid of a cluster of points in R, you can use simple statistical methods to find the mean of the x and y coordinates. This approach is effective for an unweighted centroid. If you're looking for a weighted centroid, you'll need to factor in the weights of each point in your calculations.

Here's a basic method to find the unweighted centroid:

# Sample data
xcor <- c(1, 2, 3, 4, 5)
ycor <- c(5, 4, 3, 2, 1)

# Calculating the centroid
centroid_x <- mean(xcor)
centroid_y <- mean(ycor)

print(paste("Centroid:", centroid_x, centroid_y))

For a weighted centroid, you would modify the calculation to account for the weights:

# Sample data with weights
xcor <- c(1, 2, 3, 4, 5)
ycor <- c(5, 4, 3, 2, 1)
weights <- c(1, 2, 1, 2, 1)  # Example weights

# Weighted centroid calculation
weighted_centroid_x <- sum(xcor * weights) / sum(weights)
weighted_centroid_y <- sum(ycor * weights) / sum(weights)

print(paste("Weighted Centroid:", weighted_centroid_x, weighted_centroid_y))

Additional R Package: For more advanced calculations or handling of spatial data, you might consider using the geosphere package which provides a centroid function. This can be particularly useful for geographic data.

# Assuming 'points' is a matrix or dataframe of your coordinates
centroid <- centroid(points)

Online Tool for Quick Calculations: As an additional resource, you can use the online Centroid Calculator. This tool provides a simple interface for calculating the centroid of a set of points, which can be handy for quick checks or when working outside of R.


This is excellent. I'd suggest removing outliers before doing this. For simple outlier removal, one might find the longitudes within the 75%-25% percentiles and the same for the latitudes, and only calculate mean on those values? Or for less drastic outlier removal, remove values outside the 1.5 * 75%-25% interquartile range (this is a somewhat standard outlier definition).

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