When to use this calculator
Calculate sample covariance of two paired datasets. Requires equal-length paired data and at least two pairs. Covariance depends on the measurement units.
Explore the regression & paired data calculators for other questions in this topic. For a related calculation, use the Linear Regression Intercept Calculator: Find the intercept of an ordinary-least-squares Y-on-X line.
PUTTING IT INTO PRACTICE
Covariance: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| X observations | 1,2,3 |
| Y observations | 2,4,6 |
| Result | 2 |
- Check the input labels and enter the example values above.
- Apply the relationship: Sample covariance = sum((x−mean x)(y−mean y))/(N−1)..
- The result is 2 , rounded for display.
How to interpret your result
Requires equal-length paired data and at least two pairs. Covariance depends on the measurement units.
Pair observations in the same order and use equally long lists. A least-squares line describes a linear association; it does not establish causation or guarantee future values. Outliers and extrapolation can strongly affect interpretation.
Frequently asked questions
Can a high correlation prove that one variable causes the other?
No. Association can arise through confounding, selection, coincidence or a causal relationship. Correlation alone does not identify which explanation applies.
When is the covariance calculator useful?
Calculate sample covariance of two paired datasets. Requires equal-length paired data and at least two pairs. Covariance depends on the measurement units.
How do I use the covariance calculator?
Enter x observations, y observations. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Sample covariance = sum((x−mean x)(y−mean y))/(N−1)..
What should I check before using the result?
Requires equal-length paired data and at least two pairs. Covariance depends on the measurement units.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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