Correlation Coefficient Calculator
Enter two paired lists of numbers below to instantly get Pearson's correlation coefficient (r).
How the Correlation Coefficient Is Calculated
Pearson's r divides the covariance of the two variables by the product of their standard deviations, which normalizes the result to always fall between −1 and 1 regardless of the original units.
Worked example
X: 1, 2, 3, 4, 5. Y: 2, 4, 5, 4, 5.
Working through the mean-deviation products and standard deviations gives:
r ≈ 0.7746 — a fairly strong positive relationship.
Frequently Asked Questions
What does the correlation coefficient tell you?
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, from −1 (perfect negative relationship) to 1 (perfect positive relationship). A value near 0 means little to no linear relationship.
What counts as a "strong" correlation?
There's no universal cutoff, but a common rule of thumb treats |r| above 0.7 as strong, 0.3 to 0.7 as moderate, and below 0.3 as weak — though the right threshold depends heavily on the field (social sciences tolerate weaker correlations as meaningful than physics does).
Does correlation mean causation?
No. A strong correlation only shows that two variables move together, not that one causes the other. Both could be driven by a third factor, or the relationship could be coincidental, especially with a small sample.
What's the difference between correlation and covariance?
Covariance measures how two variables move together, but its size depends on the units of the data, making it hard to compare across datasets. Correlation is covariance normalized by both variables' standard deviations, which keeps it in a fixed −1 to 1 range regardless of units.
Related Calculators
- Standard Deviation Calculator — Statistics
- Percentile Calculator — Statistics
- Mean, Median, Mode Calculator — Statistics
- Variance Calculator — Statistics