📈 Covariance Calculator

Covariance measures the direction of the linear relationship between two variables. A positive covariance means both variables tend to increase together; negative means one increases as the other decreases. The magnitude is hard to interpret without standardisation.

Correlation is a standardised version of covariance. The Pearson correlation coefficient r is always between −1 and +1, making it easier to interpret. r = Cov(X,Y) / (σ_x × σ_y).

r = 1 indicates a perfect positive linear relationship; r = −1 a perfect negative linear relationship. r = 0 suggests no linear relationship. Values close to ±1 indicate a strong linear relationship.

Sample covariance divides by n−1 (Bessel's correction) to obtain an unbiased estimator of the population covariance. Use sample covariance when your data is a sample from a larger population.

No. Correlation measures linear association, not causation. Two variables may correlate because of a common cause (confounding variable), reverse causation, or pure coincidence. Always consider the context and design of the study.