How it works
Covariance = Σ(x−x̄)(y−ȳ) / (n−1 for a sample, n for a population).
Input definitions
- X values
- Plain text; maximum 200,000 characters.
- Y values
- Plain text; maximum 200,000 characters.
- Denominator
- Choose Sample (n−1) / Population (n).
A worked example
- X values
- 1, 2, 3
- Y values
- 2, 4, 6
- Denominator
- Sample (n−1)
Assumptions & limits
At least two paired observations. Sample and population conventions differ; lists must be aligned.
Sources & review
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Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Why is covariance different from correlation?
Covariance keeps the product of the original units and changes when units change. Correlation standardizes covariance by the two standard deviations and is dimensionless.
Why can statistical results differ between tools?
Denominator, interpolation and boundary conventions can differ. Use the method and assumptions on this page to compare the same definition; displayed decimals may also be rounded.
How does the Covariance of paired data tool work?
Covariance = Σ(x−x̄)(y−ȳ) / (n−1 for a sample, n for a population).
What are the assumptions and limits of Covariance of paired data?
At least two paired observations. Sample and population conventions differ; lists must be aligned.