Covariance Calculator
Calculate how two variables vary together.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter paired X and Y datasets, each separated by commas or spaces. Both datasets must have the same number of values. The calculator computes sample covariance: the average product of deviations from each variable's mean, divided by n-1.
About Covariance
Covariance measures how two variables change together. Positive covariance means both variables tend to increase together. Negative covariance means one tends to decrease when the other increases. The magnitude depends on the scales of both variables, making it hard to compare across different variable pairs. For a standardized version, use the correlation coefficient (covariance divided by the product of standard deviations).
Frequently Asked Questions
What is the difference between covariance and correlation?
Covariance measures the direction of the linear relationship but its magnitude depends on the scales of the variables. Correlation normalizes covariance to fall between -1 and 1, making it easier to interpret and compare.
Can covariance be zero even if variables are related?
Yes. Covariance measures linear association only. Two variables with a perfect nonlinear relationship (like a parabola) can have zero covariance.
Does the order of X and Y matter?
No. Covariance is symmetric: Cov(X,Y) equals Cov(Y,X). The pairing of values matters, but swapping which variable is X and which is Y gives the same result.