Pearson Correlation Calculator
Enter two paired numeric series to calculate r, r², and a two-tailed p-value. Values can be comma or newline-separated.
Frequently asked questions
What does the Pearson correlation coefficient measure?
Pearson r measures the strength and direction of the linear relationship between two variables. It ranges from −1 (perfect negative linear relationship) to +1 (perfect positive), with 0 indicating no linear association. It does not detect curved or non-linear relationships, even strong ones. Inspect the scatter plot. If the points follow a curve rather than a line, r is not an appropriate summary.
How do I interpret the value of r?
The sign tells you direction; the magnitude tells you strength. Cohen's conventional thresholds are |r| < 0.1 negligible, 0.1–0.3 weak, 0.3–0.5 moderate, 0.5–0.7 strong, >0.7 very strong. These are rough guides, not rigid rules. In some fields a correlation of 0.3 is considered practically important; in others, 0.8 is modest.
What is r² and what does it mean?
r² is the proportion of variance in Y that is linearly explained by X. An r of 0.7 gives r² = 0.49: 49% of the variation in Y is accounted for by X. The other 51% is explained by other factors or noise. r² is often more interpretable than r for communicating practical importance.
What are the assumptions of Pearson correlation?
Both variables should be continuous. The relationship should be linear. The data should be approximately bivariate normal for the p-value to be valid, though this matters less for larger samples due to the central limit theorem. Outliers can move r substantially. Always check the scatter plot before reporting results.
Does a significant correlation prove causation?
No. A significant r means the data are unlikely under the assumption of no linear relationship. It says nothing about why the variables are related. Confounders, reverse causation, and coincidence all produce correlations. Significance is evidence of association, not mechanism.