Covariance Calculator

This calculator measures the covariance between two variables, a statistic that captures how they vary together, giving both the sample and population versions. Covariance is a building block of statistics that tells you the direction of the linear relationship between two quantities: a positive covariance means they tend to rise and fall together, a negative covariance means one tends to rise as the other falls, and a value near zero means little linear relationship. It is closely related to correlation, which is simply covariance standardised onto a fixed scale, and it underpins regression, portfolio theory in finance, where the covariance between asset returns drives diversification, and the variance-covariance matrices used throughout data science. This tool computes it directly. You paste your x values into one box and your matching y values into another, in the same order, and the calculator returns the sample covariance, which divides by one less than the number of pairs and is used when your data is a sample, and the population covariance, which divides by the number of pairs and is used when you have the whole population. It also shows the two means and the number of pairs. The results update as you type. Use it to explore the relationship between two variables, as a step toward correlation or regression, or for statistics study. Unlike correlation, covariance is not standardised, so its size depends on the units of your variables and is hard to interpret on its own; for a measure of strength that runs from minus one to plus one, follow up with the correlation coefficient. The sign of the covariance, however, immediately tells you the direction of the relationship.

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Sample covariance divides by n - 1; population covariance divides by n. Positive means the variables rise together; negative means they move oppositely.