Covariance Calculator

Covariance measures how two variables change together. A positive value means they tend to rise and fall together; a negative value means one rises as the other falls; near zero means little linear co-movement.

Both add up the same products of deviations from the means. Sample covariance divides that sum by n minus 1 (an unbiased estimate for a sample); population covariance divides by n (when your data is the whole population).

It divides the same sum of products by a smaller number, n minus 1 instead of n, so its magnitude is always slightly larger than the population value. With 5 pairs the sample is 5/4 times the population figure.

Put one x,y pair on each line and separate the two numbers with a comma, a space, or a tab. Blank lines are ignored, and every non-empty line must contain exactly two numbers.

At least two. Sample covariance divides by n minus 1, so a single pair would divide by zero. The lists of x and y values must also be equal in length since each x pairs with one y.

Correlation is covariance scaled by the two standard deviations, giving a unitless value between -1 and 1. Covariance keeps the original units and is unbounded, so its size alone does not tell you how strong the link is.

Both covariance figures are rounded to about six decimal places, and a value that computes to negative zero is shown as 0. That precision is well beyond most real data sets.

Yes. A negative covariance means the variables move in opposite directions, and a value at or near zero means no linear relationship. The direction note under the result reflects the sign of the sample value.

Yes. All parsing and calculation happen in your browser, so your numbers are never uploaded. You can even use the tool offline once the page has loaded.