Correlation Coefficient Calculator Online: Pearson, Spearman, and Kendall

Pearson, Spearman, and Kendall correlation coefficients computed in one step, with individual p-values, Pearson’s 95% confidence interval, and r².

Three coefficients measuring different things

Pearson r measures the strength of a linear relationship. It uses raw values, so it is sensitive to outliers and can only capture straight-line relationships.

Spearman ρ converts the data to ranks first, then computes Pearson. It measures monotonic relationships — as long as “when one goes up the other goes up too” holds, it does not require a straight line.

Kendall τ directly counts concordant pairs versus discordant pairs. It is more robust than Spearman, has better distributional properties in small samples, but computation scales as n².

Two examples showing why you need all three

Example 1: monotonic but non-linear. x = 1…8, y = 2ˣ: Pearson gives 0.850, while Spearman and Kendall both give 1.000. The relationship is perfectly monotonic, but Pearson underestimates it because it is not a straight line.

Example 2: a single outlier can flip the sign. x = 1, 2, …, 10 and y = 10, 9, 8, 7, 6, 5, 4, 3, 2, 50: apart from the last point, y strictly decreases with x, but that one value of 50 causes Pearson to give +0.358 and Spearman to give −0.455 — opposite signs. Looking only at Pearson leads to completely the wrong conclusion.

So: look at all three together. A large discrepancy means the data has a story. Pearson much smaller than Spearman usually means the relationship is monotonic but curved; opposite signs almost always point to an outlier.

Reading r² correctly

r² is “the proportion of variance explained by the linear relationship” — not “accuracy.” r = 0.7 looks high, but r² = 0.49, meaning half the variation is still unexplained. At r = 0.5, r² is only 0.25. The squaring makes it easy to overestimate association strength.

Correlation ≠ causation — and that’s not the whole story

Beyond “correlation does not imply causation,” two more things matter equally:

Zero correlation does not mean independence. It only means no linear (or monotonic) relationship. A U-shaped relationship can have Pearson r exactly equal to 0, yet the two variables are clearly related.

With large samples, a trivially small correlation can be statistically significant. At n = 1000, r = 0.07 can produce p < 0.05, yet it explains only 0.5% of the variance. Look at r and r² before the p-value.

Confidence interval

Pearson’s interval is computed using the Fisher z-transformation: r is first mapped to a nearly normal scale, a symmetric interval is computed there, then mapped back. The interval is therefore asymmetric around r, more visibly so as r approaches ±1. A wide interval at n < 10 is an honest reflection of uncertainty, not a flaw.