Covariance Calculator

Get the sample and population covariance of two lists, the correlation coefficient and a reading of it.

Covariance and correlation

X values

Y values

Sample covariance: —

Population covariance: —

Correlation coefficient r: —

Means: —

Pairs used: —

Interpretation: —

Sample covariance divides by n minus 1 and population covariance divides by n; the correlation is their standardised form.

Paste the first list of values into the X box.
Paste the matching values into the Y box, in the same order.
Read the sample and population covariance, the correlation and the interpretation.

Common questions about the free online covariance calculator.

Paste the two lists of paired values and the tool reports the sample and population covariance together with the correlation coefficient.

Sample covariance is the sum of the products of the paired deviations, divided by n minus 1, which corrects for the sample size.

Population covariance uses the same sum of paired deviations but divides by n, because the whole population is assumed known.

A positive covariance means the two variables tend to rise together, while a negative one means they tend to move in opposite directions.

Covariance depends on the units of the data, so its size has no fixed scale. The correlation coefficient removes that problem.

r is the population covariance divided by the product of the two population standard deviations, giving a value between -1 and 1.

Values near 1 or -1 are strong, values near 0 are weak, and the sign shows whether the relationship is positive or negative.

Yes. The tool pairs values in order and stops at the shorter list, and the number of pairs actually used is reported for you.

If a list has no variation its standard deviation is zero, so the correlation is undefined and the tool says so instead of dividing by zero.

No, the covariance calculator runs entirely in your browser and never sends the numbers anywhere.

Last updated: October 10, 2026