Correlation Test Calculator
Correlation test calculator works out Number of pairs and Pearson's r from X values, Y values and Coefficient. The default figures on this page give pearson's r of 0.774597; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
7 steps
- n = 5 pairs. Mean of X = 3, mean of Y = 4.
- Sxx = sum (x - xbar)^2 = 10; Syy = 6; Sxy = sum (x - xbar)(y - ybar) = 6.
- r = Sxy / sqrt(Sxx x Syy) = 6 / sqrt(10 x 6) = 0.77459667
- Spearman's rho = Pearson's r applied to the midranks = 0.73786479
- Kendall: 7 concordant and 1 discordant pairs out of 10, giving tau-b = 0.67082039.
- t = r sqrt(n - 2) / sqrt(1 - r^2) = 2.12132034 on 3 degrees of freedom, two-sided p = 0.12402706.
- Fisher z = arctanh(r) = 1.03171853; 95% interval for rho = [-0.340082, 0.984236].
Its 4 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the correlation test calculator calculates
Computes Pearson's r, Spearman's rank correlation rho, Kendall's tau-b and cosine similarity for two paired data sets, with covariance, the coefficient of determination, a t test of significance and a Fisher z confidence interval for the population correlation.
How to use this correlation test calculator
Enter X values, Y values, Coefficient and Confidence level. Number of pairs updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Number of pairs, Pearson's r and Coefficient of determination (r squared).
The method follows NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.13 Correlation and Scatter Plots, Kendall, M.G. (1945), "The treatment of ties in ranking problems", Biometrika 33(3), 239-251, Fisher, R.A. (1921), "On the probable error of a coefficient of correlation deduced from a small sample", Metron 1, 3-32 and Evans, J.D. (1996), Straightforward Statistics for the Behavioral Sciences, Brooks/Cole.
What you can compare
Change one input at a time to see how it affects Number of pairs, Pearson's r and Coefficient of determination (r squared). The inputs you can vary are X values, Y values, Coefficient and Confidence level.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
How do I calculate the correlation?
Computes Pearson's r, Spearman's rank correlation rho, Kendall's tau-b and cosine similarity for two paired data sets, with covariance, the coefficient of determination. Open “How this is worked out” beside the result to see each step for your own figures.
How to calculate correlation in a calculator?
It needs X values, Y values, Coefficient and Confidence level. Nothing else is required, and the figures stay in your browser.
What is a good correlation score?
Computes Pearson's r, Spearman's rank correlation rho, Kendall's tau-b and cosine similarity for two paired data sets, with covariance, the coefficient of determination. On this page it is computed from X values, Y values and Coefficient and shown as Number of pairs, Pearson's r and Coefficient of determination (r squared).
What does 95% correlation mean?
The result gives Number of pairs, Pearson's r, Coefficient of determination (r squared), Spearman's rho, Kendall's tau-b and Cosine similarity, each labelled with its unit so the figure can be read on its own.
What information do I need for the correlation test calculator?
You need X values, Y values, Coefficient and Confidence level. The page opens with default figures that give pearson's r of 0.774597, so you can see the scale before entering your own.
What does this correlation test calculator show?
It shows Number of pairs, Pearson's r, Coefficient of determination (r squared), Spearman's rho, Kendall's tau-b, Cosine similarity, Sample covariance and Population covariance, with the working and any warnings for your entries.