Correlation Coefficient Calculator

In short Pearson's r measures how close two variables come to a straight-line relationship, on a scale from −1 to +1. The eight pairs loaded above give r = 0.9653 and r² = 0.9318, meaning 93.18% of the variation in y is accounted for by the straight-line relationship with x. The tool also gives Spearman's rho, which is Pearson's r computed on the ranks, and a confidence interval for r built through Fisher's z transform — a plain ± interval would run off the end of the scale near ±1, because the sampling distribution of r is skewed there. Two limits matter more than the number. Pearson's r measures STRAIGHT-LINE association only: a symmetric parabola has r of exactly zero while y is completely determined by x, so a small r rules out a linear relationship and nothing else. And r is not robust — a single far-out pair can move it from near zero to near one. That is the point of Anscombe's quartet, four data sets with identical correlations and completely different shapes, and it is why plotting the data is not optional. A large gap between Pearson and Spearman is the quickest tell that the relationship is curved or that one point is doing all the work. Finally, the significance test here is the same t-test the regression slope reports, because "r is not zero" and "the slope is not zero" are one hypothesis. And correlation still is not causation: x causing y, y causing x, and something else causing both all produce the same r.