Covariance Calculator
How two variables move together, before standardising.
Enter your values
ⓘ Live results
Results
- Sample covariance
- 13.5
- Population covariance
- 10.8
- Correlation r
- 0.98722
- Direction
- Positive — they rise together
- Mean of X / Y
- 6 / 8.8
- Sum of products
- 54
Quick answer
Covariance measures whether two variables move together: positive means they rise together, negative means one falls as the other rises.
cov = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ (n − 1)
How to use the Covariance Calculator
- 1Enter the X values in order.
- 2Enter the matching Y values.
- 3Read covariance for direction and correlation for strength on a −1 to +1 scale.
Worked example
Using the values the calculator loads with:
Inputs
- X values2, 4, 6, 8, 10
- Y values3, 7, 8, 12, 14
Results
- Sample covariance13.5
- Population covariance10.8
- Correlation r0.98722
- DirectionPositive — they rise together
- Mean of X / Y6 / 8.8
- Sum of products54
Frequently asked questions
Why is covariance hard to interpret?
Its size depends on the units — change metres to centimetres and covariance jumps 100-fold. Correlation fixes that.
Does zero covariance mean independence?
Not necessarily. It rules out a linear relationship, but a perfect U-shape can still have zero covariance.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.