Spearman Rho Calculator

Enter paired data

Formula used

When there are no ties, Spearman's rho can be calculated with the classic shortcut:

ρ = 1 − [6 × Σd²] / [n(n² − 1)]

Where:

• ρ is Spearman's rank correlation coefficient.
• d is the difference between paired ranks.
• n is the number of paired observations.

When ties exist, this calculator ranks tied observations using average ranks, then computes:

ρ = corr(Rx, Ry)

That is the Pearson correlation between X ranks and Y ranks. This method is more reliable for tied data.

For significance, the calculator uses the common approximation:

t = ρ × √[(n − 2) / (1 − ρ²)]

The p-value is then derived from the t distribution with n − 2 degrees of freedom.

How to use this calculator

1. Enter a label for each variable if you want custom headings.
2. Paste X values into the first box.
3. Paste Y values into the second box in the same order.
4. Choose alpha, confidence level, alternative hypothesis, and decimal precision.
5. Click Calculate Spearman Rho.
6. Read rho, p-value, confidence interval, tie summary, and the rank table.
7. Use the CSV or PDF buttons to export the result.
8. Review the Plotly graph to inspect the ranked relationship visually.

Example data table

This sample shows a strong positive monotonic relationship. You can load it directly with the example button.

Expected rho for this example is about 0.9762.

FAQs