Mihsaba
العربيةEnglishEspañolFrançais
Mihsaba›Covariance Calculator

Covariance Calculator

Calculate sample or population covariance from two equal-length datasets, with both means and Pearson correlation for context.

The result is mathematical and depends on test assumptions and sampling; it does not replace statistical interpretation of the real context.

How to use

Covariance measures the direction of joint variation between two variables. Enter equal-length datasets and choose sample or population mode. A positive sign means the variables tend to move together, a negative sign means opposite movement, while magnitude depends on the measurement units.

  1. Enter X values.
  2. Enter Y values with the same count and matching order.
  3. Choose sample to divide by n−1 or population to divide by n.
  4. Review covariance, means and r for context.

How it is calculated

Sample: Cov=Σ[(x−x̄)(y−ȳ)]/(n−1); population divides by n

Example

Example: X={1,2,3,4,5} and Y={2,4,5,4,5}. In sample mode, mean X=3 and mean Y=4; paired deviations from those means are multiplied and summed before division by n−1.

Important notes

Do not compare covariance magnitudes directly across datasets with different units. Correlation standardizes the relationship to −1 through 1. Neither covariance nor correlation proves causation.

Frequently asked questions

Sample versus population covariance?

Sample covariance divides by n−1; population covariance divides by n.

Does covariance have units?

Yes. Its unit is the product of the X and Y units.

Why show correlation too?

Correlation removes scale effects and provides context for covariance.

Does positive covariance mean a strong relationship?

Not necessarily; covariance magnitude depends on units.