When to use this calculator
Measure linear association between two equal-length numeric datasets. Both variables need nonzero variance. Correlation does not establish causation and is sensitive to outliers.
Explore the regression & paired data calculators for other questions in this topic. For a related calculation, use the Normal Confidence Interval Margin Calculator: Calculate the margin around a mean from a supplied z critical value.
PUTTING IT INTO PRACTICE
Pearson Correlation: 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 | 1 |
- Check the input labels and enter the example values above.
- Apply the relationship: r = covariance(X,Y)/√(variance(X) × variance(Y))..
- The result is 1 , rounded for display.
How to interpret your result
Both variables need nonzero variance. Correlation does not establish causation and is sensitive to outliers.
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 pearson correlation calculator useful?
Measure linear association between two equal-length numeric datasets. Both variables need nonzero variance. Correlation does not establish causation and is sensitive to outliers.
How do I use the pearson correlation 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?
r = covariance(X,Y)/√(variance(X) × variance(Y))..
What should I check before using the result?
Both variables need nonzero variance. Correlation does not establish causation and is sensitive to outliers.
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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