Skip to content
ENExplore Calculators

Adjusted Rand Index Calculator

Work out adjusted rand index instantly with clear inputs, formula shown and shareable results.

About Adjusted Rand Index Calculator

The Rand index counts pairs of points that two partitions agree about, but even random labellings agree on many pairs. The adjusted version subtracts the expected agreement and rescales, so a random clustering scores about 0, a perfect match scores 1, and systematically worse-than-random assignments go negative. That correction is what makes ARI comparable across different numbers of clusters.

Formula

Adjusted Rand index

ARI = (index - expected index) / (max index - expected index)

Worked example

With the default values below, Adjusted Rand Index Calculator returns Adjusted Rand index of 0.5000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Observed pair agreements (Rand index numerator)minimum 0
120
Expected agreements under random labellingminimum 0
40
Maximum possible agreementsminimum 1
200

Results

Adjusted Rand index
0.5000
Unadjusted Rand index
0.6000
Agreements expected by chance
40.00
Agreement level
Moderate agreement

Step by step

  1. 1Values used
  2. 2Adjusted Rand index
  3. 3Adjusted Rand index= 0.5000
  4. 4Unadjusted Rand index= 0.6000
  5. 5Agreements expected by chance= 40.00
  6. 6Agreement level= Moderate agreement

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why can ARI be negative?

Because the expected agreement is subtracted. A partition that splits genuine groups apart more than chance would gives a value below zero.

Does ARI need the same number of clusters in both partitions?

No. It compares pairwise co-membership, so it works when the predicted clustering has more or fewer groups than the reference labels.

Related Calculators

Adjusted Rand Index Calculator | Calcrivo