Covariance Calculator

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Separate values with commas, spaces or new lines.
Must contain the same number of values as X. Each pair (x, y) is read in order.
Use sample (n-1) when your data is a subset of a larger population. Use population (n) when your data is the entire group.
CovarianceStrong positive correlation
13
Pearson correlation (r)0.9884
Mean of X6
Mean of Y8.6
Std dev of X3.1623
Std dev of Y4.1593
Variance of X10
Variance of Y17.3
Population covariance10.4
Sample covariance13
Pairs (n)5
Variance of X10
Variance of Y17.3
Covariance13

Sample covariance is 13.0000, indicating a positive relationship: as X increases, Y tends to increase. The Pearson r of 0.9884 places this on a scale of -1 to +1, making the strength easy to compare across different data sets.

  • Covariance reveals only the direction of a linear relationship. Its magnitude depends on the units of X and Y and cannot be compared across different data sets.
  • Sample covariance (n-1) is the right choice when your data is a subset of a larger population. It corrects the downward bias that would arise from dividing by n.
  • The Pearson correlation r standardizes covariance by the product of the two standard deviations, giving a unit-free value between -1 and +1 that measures the strength of the linear relationship.
  • The standard deviations are 3.1623 (X) and 4.1593 (Y), and the variances are 10 (X) and 17.3 (Y).

Next stepUse the Pearson r value to compare the strength of this relationship against other paired data sets, or feed the covariance into a portfolio risk calculation.

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