Cluster Size Calculator
Estimate cluster membership counts from balanced, weighted, geometric, power, or manual distributions. Review size dispersion, concentration, entropy, effective cluster count, and export-ready results for segmentation, prototype analysis, or unsupervised learning reviews.
Calculator Inputs
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Example Data Table
This example uses 1,200 samples, five clusters, and weighted percentages of 30%, 25%, 20%, 15%, and 10%.
| Cluster | Weight (%) | Estimated size | Share (%) | Cumulative share (%) |
|---|---|---|---|---|
| Cluster 1 | 30.00 | 360 | 30.00 | 30.00 |
| Cluster 2 | 25.00 | 300 | 25.00 | 55.00 |
| Cluster 3 | 20.00 | 240 | 20.00 | 75.00 |
| Cluster 4 | 15.00 | 180 | 15.00 | 90.00 |
| Cluster 5 | 10.00 | 120 | 10.00 | 100.00 |
Formula Used
1) Normalize the weights
For any input mode, each cluster gets a weight wi. The normalized share becomes pi = wi / Σw. Balanced mode uses identical weights. Weighted, geometric, and power modes derive weights from user settings.
2) Convert shares into integer sizes
The raw allocation is ri = N × pi, where N is total samples. Integer counts start with floor(ri). Remaining samples are assigned to the largest fractional remainders so the final sum still equals N.
3) Measure spread and imbalance
Average size is N / K. Standard deviation is √(Σ(si − mean)² / K). Coefficient of variation is std / mean. Imbalance ratio is max(si) / min(si) when the smallest cluster is not zero.
4) Evaluate concentration and diversity
Entropy is H = −Σ(pi ln pi). Normalized entropy is H / ln(K). Effective clusters equal eH. Gini coefficient uses pairwise size differences divided by 2KΣsi to describe inequality.
How to Use This Calculator
- Enter the total sample count and the number of desired clusters.
- Select a distribution mode that matches your clustering assumption or observed allocation pattern.
- Provide mode-specific values, such as percentages, a geometric ratio, a power exponent, or manual counts.
- Set the minimum acceptable share threshold to flag undersized groups.
- Choose whether manual counts should be normalized and whether results should be sorted from largest to smallest.
- Press Calculate Cluster Sizes to display the result block above the form.
- Review the summary metrics, allocation table, warnings, and concentration measures.
- Use the CSV or PDF buttons to export the visible results.
FAQs
1) What does this calculator estimate?
It estimates how many samples belong to each cluster after applying a chosen distribution pattern. It also measures balance, concentration, dispersion, and effective cluster diversity for model review or segmentation planning.
2) When should I use weighted percentages?
Use weighted percentages when you already know approximate membership shares from prior experiments, business assumptions, or historical segmentation patterns. The calculator normalizes the values automatically, even when they do not total exactly one hundred.
3) What is geometric decay useful for?
Geometric decay is useful when each next cluster is expected to be a constant fraction of the previous one. This often models strongly ranked segment sizes or descending prototype occupancy patterns.
4) Why is power-law mode included?
Power-law mode fits long-tail situations where a few clusters dominate while many smaller clusters remain. Adjusting the exponent helps simulate mild or severe concentration across ordered groups.
5) What does effective cluster count mean?
Effective cluster count converts entropy into an intuitive diversity number. If five clusters exist but one dominates heavily, the effective count may behave more like two or three meaningful groups.
6) How should I read the Gini coefficient?
A lower Gini coefficient means cluster sizes are more even. A higher value signals stronger inequality, which may indicate imbalance, over-segmentation, sparse clusters, or weak sampling coverage.
7) Why can a cluster be flagged as undersized?
A cluster is flagged when its percentage falls below your minimum acceptable share threshold. That warning helps identify groups that may be unreliable for downstream training, validation, or interpretation.
8) Can I export the results for reports?
Yes. The CSV button exports summary metrics and the per-cluster table. The PDF button captures the visible result section so you can save or share a formatted report snapshot.