Covariance Calculator
Calculate sample or population covariance between two paired datasets.
About Covariance Calculator
Covariance measures how two variables change together. Positive covariance indicates they tend to increase together; negative means one tends to decrease when the other increases. Unlike correlation, covariance is not bounded to [−1, 1].
Formula
Cov(X,Y) = Σ(xᵢ−x̄)(yᵢ−ȳ) / (n−1)
- xᵢ,yᵢ
- Paired data points
- x̄,ȳ
- Means
- n
- Sample size
Worked example
With the default values below, Covariance Calculator returns Covariance of 6.666667. Change any input above and every figure here is recalculated in your browser.
Inputs used
- X values (comma separated)
- 2, 4, 6, 8
- Y values (comma separated)
- 1, 3, 5, 7
- Typeone of Sample (n−1), Population (n)
- Sample (n−1)
Results
- Covariance
- 6.666667
- Mean of X
- 5.0000
- Mean of Y
- 4.0000
Step by step
- 1Values used
- 2Formula applied
- 3Covariance= 6.666667
- 4Mean of X= 5.0000
- 5Mean of Y= 4.0000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does covariance relate to correlation?
Correlation is the standardized form of covariance: r = Cov(X,Y) / (σₓ × σᵧ). This removes the effect of scale.
Can covariance be greater than 1?
Yes, covariance is unbounded. Its magnitude depends on the scales of X and Y. That's why correlation (bounded −1 to 1) is often preferred.