Adjusted Rand Index Calculator

Calculator Form

Paste one label per line, or separate labels with commas, spaces, or semicolons.

Dataset Name

Input Guidance

Observation counts must match exactly.

Export Options

Label Set A

This could be ground truth, baseline clusters, or reference grouping.

Label Set B

This could be predicted clusters, model output, or alternative partitioning.

Example Data Table

Observation	Label Set A	Label Set B
1	A	1
2	A	1
3	A	2
4	B	2
5	B	2
6	B	2
7	C	3
8	C	3
9	C	3
10	D	4
11	D	4
12	D	1

Use the Load Example button to populate this dataset and generate all charts and statistics.

Formula Used

Adjusted Rand Index:

ARI = (Index − Expected Index) / (Max Index − Expected Index)

Using the contingency table cell counts n_ij, row totals a_i, and column totals b_j:

Index = Σ C(n_ij, 2)

Expected Index = [Σ C(a_i, 2) × Σ C(b_j, 2)] / C(n, 2)

Max Index = 0.5 × [Σ C(a_i, 2) + Σ C(b_j, 2)]

Here, C(x, 2) = x(x − 1) / 2. ARI ranges roughly from negative values up to 1, where 1 means identical clustering.

ARI corrects the Rand Index for chance, so random partitions tend to score near zero rather than appearing artificially strong.

How to Use This Calculator

Enter a dataset name if you want a custom heading in exports.
Paste Label Set A values in the first textarea.
Paste Label Set B values in the second textarea.
Keep both lists aligned observation by observation.
Use one label per line, or separate labels with commas.
Click Calculate ARI to generate metrics and charts.
Review the contingency table and pair breakdown.
Export CSV for raw metrics or PDF for a polished report.

Frequently Asked Questions

1. What does the Adjusted Rand Index measure?

It measures how similarly two clustering label assignments group the same observations, while correcting for agreement that could happen by random chance.

2. What is a good ARI score?

Scores near 1 indicate very strong agreement. Scores around 0 suggest chance-level similarity. Negative values indicate agreement worse than random expectation.

3. Can the two label sets use different names?

Yes. Cluster labels do not need matching names. The calculator compares grouping structure, not literal label text.

4. Why must both lists have the same length?

Each position represents the same observation across both label sets. Unequal lengths break that one-to-one pairing and make ARI invalid.

5. Does ARI work for binary and multiclass clustering?

Yes. ARI works with two clusters, many clusters, balanced clusters, and uneven cluster sizes, as long as both lists reference identical observations.

6. How is ARI different from the Rand Index?

The Rand Index measures raw pair agreement. ARI adjusts that agreement for chance, giving a more trustworthy score when partitions are random or imbalanced.

7. Can I use this for model evaluation?

Yes. ARI is often used to compare predicted clusters against reference labels or to compare outputs from different clustering algorithms.

8. What does the contingency table show?

It shows how observations from each cluster in Label Set A distribute across clusters in Label Set B, helping you inspect overlap and fragmentation.