What does Spearman's rho measure?

Spearman's rho (ρ) measures the strength and direction of a monotonic relationship: whether Y tends to rise (or fall) as X rises, not necessarily in a straight line. It runs from −1 (perfectly decreasing) through 0 (no monotonic trend) to +1 (perfectly increasing). Common rough labels are |ρ| < 0.3 weak, 0.3–0.7 moderate and above 0.7 strong, but the field and sample size matter.

How is rho calculated, and why does the d² formula give a different answer?

Rank each variable (ties get the average rank), then compute the Pearson correlation of the ranks. The shortcut ρ = 1 − 6Σd² ÷ (n(n² − 1)) is algebraically identical only when there are no ties. With ties it overstates the correlation slightly, so statistical software (R cor(method = "spearman"), SPSS, SciPy) uses the Pearson-on-ranks value, as this calculator does.

How is the p-value computed?

For larger samples rho is converted to t = ρ√((n − 2) ÷ (1 − ρ²)) and compared with a t distribution with n − 2 degrees of freedom, the method used by most software. For n ≤ 10 the calculator also computes the exact permutation p-value: the share of all n! re-orderings of Y whose |ρ| is at least as large as observed. Prefer the exact value for small samples.

One-tailed or two-tailed?

Use two-tailed unless you stated the direction (positive or negative) before collecting the data. A one-tailed p-value is half the two-tailed value when the observed rho has the predicted sign, and close to 1 when it has the opposite sign.

How do I paste data from Excel or Google Sheets?

Select the two columns (with or without a header), copy, and paste into the "Paste two columns" box, then press "Use columns". Tabs, commas, semicolons and spaces all work as separators. Rows where either value is blank or non-numeric are skipped and counted, so the pairs stay aligned.

How many data points do I need?

At least 3 pairs to compute a p-value and 4 for a confidence interval. With n = 5 only ρ = ±1 reaches two-tailed p < 0.05 by the exact test (p = 0.017). Around 30 pairs give reasonable power to detect a moderate correlation (ρ ≈ 0.5).

How do I report a Spearman correlation?

APA style: "There was a strong positive correlation between hours studied and exam rank, rₛ(6) = .93, p = .002." The number in brackets is the degrees of freedom, n − 2, and for n ≤ 10 the exact p-value is preferred. Add the confidence interval when possible: 95% CI [.63, .99]. These are the numbers for the 8-pair example on this page.

Spearman Rank Correlation Calculator

Paste two columns or two lists to get Spearman's rho (Pearson r of mid-ranks, so ties are handled exactly), the two- or one-tailed p-value from the t approximation and, for n ≤ 10, the exact permutation p-value, plus a confidence interval and the rank table.

Enter Your Data

Paste two columns (Excel, Sheets, CSV)

X Variable (comma-separated numbers)

Y Variable (same length as X)

Significance (α)

Test

Enter data on the left and click Calculate to see results.

Rho (ρ)

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p-value

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t-stat

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Details

p (t approximation)
p (exact permutation)
95% CI for ρ
1 − 6Σd²/(n(n²−1))
Tied values (X / Y)
Σd²

Rank Scatter Plot

Ranked X vs Ranked Y

Rank Table

#	X	Rank X	Y	Rank Y	d²

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Summary

The Spearman Rank Correlation Calculator computes Spearman's rho (ρ), the nonparametric measure of a monotonic association, entirely in your browser. Paste two columns from a spreadsheet or two comma-separated lists; the tool ranks both with mid-ranks for ties, takes the Pearson correlation of the ranks, and reports the t statistic, degrees of freedom, a one- or two-tailed p-value, the exact permutation p-value for up to 10 pairs, a Fisher-z confidence interval, the d² shortcut for comparison, a rank table and a rank scatter plot.

How it works

Paste two columns copied from a spreadsheet or CSV (a header row is detected and rows with a missing value are dropped), or type the X and Y lists separately.
Each variable is ranked from smallest to largest; tied values share the average of the ranks they span (mid-ranks).
Rho is the Pearson correlation of the two rank vectors. Without ties this equals 1 − 6Σd² ÷ (n(n² − 1)); with ties only the Pearson-on-ranks value is correct, and the tool shows both.
The t approximation uses t = ρ√((n − 2) ÷ (1 − ρ²)) with n − 2 degrees of freedom. For n ≤ 10 the tool also enumerates every permutation of Y (up to 3,628,800) to give the exact p-value.
The confidence interval uses the Fisher z transform with the Fieller–Hartley–Pearson standard error √(1.06 ÷ (n − 3)).
Choose a two-tailed test, or a one-tailed test when you predicted the direction before seeing the data.

Use cases

Test whether student rankings on two exams agree.
Correlate Likert-scale or other ordinal survey answers.
Measure agreement between two judges' scores in a competition.
Check a monotonic but non-linear relationship, such as dose and response.
Analyse small samples or data with outliers where Pearson's assumptions fail.
Report rho, p and a confidence interval in APA style for a thesis or assignment.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu