Covariance Calculator
Calculate the covariance between two variables from paired data. Choose between population and sample covariance, and see the corresponding Pearson correlation coefficient to assess the strength and direction of the linear relationship.
Covariance measures the joint variability of two random variables. When two variables tend to increase together, the covariance is positive. When one tends to increase as the other decreases, the covariance is negative. A covariance near zero suggests little linear association.
The formula is Cov(X,Y) = Σ(xi - x̄)(yi - ȳ) / n for population covariance, or divided by (n-1) for sample covariance. The sample version corrects for the bias that arises when estimating from a subset of the population, using Bessel's correction.
One limitation of covariance is that its magnitude depends on the units of measurement, making it hard to compare across different datasets. The Pearson correlation coefficient normalizes the covariance by dividing by the product of the standard deviations, producing a unitless measure between -1 and +1 that is easier to interpret.