Cluster Centroid Calculator
Enter up to ten points, choose 2 to 5 dimensions, optionally apply weights, and calculate centroid coordinates with spread diagnostics.
Example Data Table
This sample illustrates a 3-dimensional weighted cluster. Use the Load Example button to populate similar values into the calculator.
| Point | X1 | X2 | X3 | Weight |
|---|---|---|---|---|
| P1 | 2.0 | 3.5 | 1.2 | 1.0 |
| P2 | 3.0 | 4.1 | 1.8 | 1.2 |
| P3 | 4.4 | 5.0 | 2.2 | 0.9 |
| P4 | 5.2 | 4.8 | 2.7 | 1.5 |
| P5 | 3.8 | 3.9 | 1.9 | 1.1 |
Formula Used
The calculator uses the weighted centroid formula for each dimension. When weighting is disabled, every point receives weight 1, so the centroid becomes the arithmetic mean.
Euclidean distance for point i: di = √(Σ (xij - Cj)²)
WCSS = Σ wi × di²
Variance for dimension j = (Σ wi × (xij - Cj)²) / (Σ wi)
These measures help you understand the central location, compactness, and dimensional spread of a cluster across multiple variables.
How to Use This Calculator
- Enter a cluster name so the report is easy to identify.
- Choose the number of dimensions needed for your point data.
- Select weighted or unweighted centroid mode.
- Set the output precision for displayed metrics.
- Fill at least two complete points with all required coordinates.
- Enter positive weights when weighted mode is active.
- Press Calculate Centroid to show the result above the form.
- Use the CSV or PDF buttons to export the generated report.
Frequently Asked Questions
1. What is a cluster centroid?
A cluster centroid is the central point representing a group of observations. It is usually the mean position across all included dimensions.
2. When should I use weighted centroids?
Use weighted centroids when some observations should influence the center more strongly, such as larger populations, stronger memberships, or confidence-adjusted points.
3. What does WCSS mean?
WCSS means within-cluster sum of squares. It measures total squared distance from points to the centroid and helps indicate cluster compactness.
4. Can I use more than three dimensions?
Yes. This calculator supports 2, 3, 4, or 5 dimensions, making it suitable for many practical clustering and segmentation tasks.
5. Why are some rows ignored?
Rows with every coordinate left blank are ignored. Partially filled rows trigger an input warning because complete coordinates are required.
6. Is the centroid always an existing point?
No. A centroid is usually a calculated center. It may fall between observed points and often does not match any single original row.
7. What distance method is used here?
The diagnostic section uses Euclidean distance from each point to the centroid. That is a common choice for geometric clustering summaries.
8. Can I export the results?
Yes. After calculation, you can download a CSV summary or create a PDF report containing the centroid table and point diagnostics.