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Spearman Rank Correlation from Σd² Calculator

ρ = 1 − 6 · Σd² / (n · (n² − 1)) for tied-free ranks.

Compute the Spearman rank-order correlation coefficient ρ from the sum of squared rank differences and the number of pairs: ρ = 1 − 6·Σd² / (n·(n² − 1)). Assumes all ranks are distinct (no ties).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

ρ = 1 − 6·Σd² / (n·(n² − 1))

In depth

Compute the Spearman rank-order correlation coefficient ρ from the sum of squared rank differences and the number of pairs: ρ = 1 − 6·Σd² / (n·(n² − 1)). Assumes all ranks are distinct (no ties).