Covariance calculator
Paste paired X and Y values and choose whether they form a sample or the complete population.
Covariance components
| Row | X | Y | X − mean X | Y − mean Y | Deviation product |
|---|---|---|---|---|---|
| Fill in the fields above — the result is computed on this page. | |||||
How to use this page
- Paste matching X and Y values.
- Choose sample or population.
- Read covariance and inspect the components table.
What this page does not do: Covariance and correlation describe linear association and do not establish causality. The order of X and Y must refer to the same cases.
Further reading
Covariance measures the direction of joint variation between two variables. A positive value means high X values tend to accompany high Y values, while a negative value indicates the opposite direction.
Its magnitude depends on the units and scale of both variables. The calculator therefore also reports Pearson correlation, which standardises the result to the range from −1 to 1 when both variables have nonzero spread.
Frequently asked questions
When should I divide by n − 1?
Use it when the data is a sample and covariance estimates the population covariance. Select n for the complete population.
Why is covariance not limited to −1 and 1?
It retains the variables' units and scale. Pearson correlation is the standardised counterpart.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).