Research Workbench

Mahalanobis distance from a reference distribution

Measure multivariate distance using a supplied center and covariance.

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First row center; next p rows covariance; remaining rows observations

Use 2–10 dimensions. Supply p covariance rows after the center, then 1–100 synthetic observation rows. The covariance must be positive definite.

The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.

Calculation results

Squared distances in row order: 1.3333333, 5.3333333, 0.0000000
Distances in row order: 1.1547005, 2.3094011, 0.0000000
Maximum squared distance: 5.3333333

How to interpret the output

Squared distance is (x−center)ᵀ covariance⁻¹(x−center). It reflects scale and correlation relative to the supplied reference. No automatic outlier cutoff is applied: chi-square thresholds need distribution and estimation assumptions. An unusual point is not necessarily an error and should not be deleted mechanically.

Method reference

Source checked 2026-11-06. Read the reproducible calculator validation report.