How does the Covariance Calculator work?

Sample covariance: Cov(X,Y) = Σ(xᵢ−x̄)(yᵢ−ȳ) / (n−1) Then: Positive: variables move together Then: Negative: variables move oppositely Then: Zero: no linear relationship.

Can you give an example of how to use the Covariance Calculator?

Example: Input X=[2,4,4,4,5], Y=[1,3,3,4,4] gives a result of Cov ≈ 0.95 (positive relationship).

Is the Covariance Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Covariance Calculator?

Our Covariance Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Covariance Calculator

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Covariance

4.4286

Correlation (r)

0.9764

8

Correlation: Strong positive

Covariance measures how two variables change together. Positive covariance means they tend to increase together; negative means one increases as the other decreases. It is the foundation of correlation and portfolio theory.

Symbol	Name	Unit	Description
X, Y	two variables/datasets	—	—
μₓ, μᵧ	means of X and Y	—	—
Cov(X,Y)	covariance	—	measure of joint variability
n	number of data points	—	—

Sign	Meaning	Example
Positive	Variables increase together	Height & weight
Negative	Inverse relationship	Price & demand
Zero	No linear relationship	Shoe size & IQ
Normalised = r	Correlation coefficient	−1 to +1 range

References

›Covariance — Khan Academy

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