Pearson Correlation Calculator

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation). It is the most widely used measure of linear association in statistics.

Both variables should be continuous and measured on interval or ratio scales. The relationship between them should be linear, both variables should be approximately normally distributed, there should be no significant outliers, and you need at least 3 pairs of observations. Violating these assumptions may make Spearman's rho a better choice.

r² tells you what proportion of the variance in one variable is explained by the other. For example, an r of 0.8 gives an r² of 0.64, meaning 64% of the variability in Y can be explained by X. The remaining 36% is due to other factors.

The null hypothesis (H₀) states that the population correlation coefficient ρ (rho) equals zero — meaning there is no linear relationship between the two variables. A significant p-value (below your chosen α) leads you to reject this hypothesis and conclude a real correlation likely exists.

If the p-value is less than your chosen significance level (α), the correlation is statistically significant — meaning it is unlikely to have occurred by chance. For example, with α = 0.05, a p-value of 0.03 means there is only a 3% probability of observing this correlation if no real relationship existed.

Use a two-tailed test when you have no prior hypothesis about the direction of the correlation (positive or negative). Use a one-tailed test only if you predicted the direction before collecting your data. Two-tailed tests are more conservative and are the standard choice in most research contexts.

Common benchmarks (Cohen, 1988): |r| < 0.1 is negligible, 0.1–0.3 is weak, 0.3–0.5 is moderate, 0.5–0.7 is strong, and |r| > 0.7 is very strong. However, what counts as meaningful depends on the field — small correlations can be highly important in some disciplines.

Use Pearson's r when both variables are continuous, normally distributed, and you expect a linear relationship. If your data are ordinal, heavily skewed, or contain significant outliers, consider Spearman's rank correlation instead. For nominal/categorical data, consider Cramér's V or the phi coefficient.