Spearman Rank Correlation Calculator

Work out spearman rank correlation instantly with clear inputs, formula shown and shareable results.

About Spearman Rank Correlation Calculator

Spearman's ρ is Pearson's correlation applied to the ranks rather than the raw values, so it detects any monotonic relationship and resists outliers. With no tied ranks the shortcut 1 − 6Σd²/(n(n² − 1)) gives the same answer.

Formula

Spearman's rho

ρ = Pearson correlation of the ranks = 1 − 6Σd² / (n(n² − 1)) when there are no ties

Worked example

With the default values below, Spearman Rank Correlation Calculator returns Spearman's ρ of -0.17575758. Change any input above and every figure here is recalculated in your browser.

Inputs used

First variable: 86, 97, 99, 100, 101, 103, 106, 110, 112, 113
Second variable: 2, 20, 28, 27, 50, 29, 7, 17, 6, 12

Results

Spearman's ρ: -0.17575758
ρ from 1 − 6Σd²/(n(n²−1)): -0.17575758
Σd²: 194.0000
Number of pairs: 10

Step by step

1Values used
2Spearman's rho
3Spearman's ρ= -0.17575758
4ρ from 1 − 6Σd²/(n(n²−1))= -0.17575758
5Σd²= 194.0000
6Number of pairs= 10

Assumptions and limits

The result is derived only from the 2 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 8 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

For the classic sample data?

ρ ≈ −0.1758, a weak negative monotonic association.

When is Spearman better than Pearson?

When the relationship is monotonic but curved, or when outliers would distort Pearson's r.