Correlation Coefficient Calculator
Calculate the Pearson correlation coefficient (r) between two variables.
Enter numbers separated by commas, spaces, or new lines. Both lists must contain the same number of values (n ≥ 2).
Correlation (r)
R-Squared (r²)
Data Points (n)
Interpretation
Best-Fit Line & Statistics
Regression Line
Mean of X (x̄)
Mean of Y (ȳ)
Slope (b)
What the Pearson Correlation Coefficient Means
The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It always falls between −1 and +1. A value of +1 indicates a perfect positive linear relationship, −1 indicates a perfect negative one, and 0 means no linear relationship at all. It is calculated as:
r = [ n·Σxy − Σx·Σy ] / √( [n·Σx² − (Σx)²]·[n·Σy² − (Σy)²] )
Correlation vs. Causation
A high correlation does not mean one variable causes the other. Two variables may move together because of coincidence, a shared third factor (a confounder), or reverse causation. Always interpret correlation in context and use controlled experiments or further analysis before drawing causal conclusions.
Interpreting R-Squared (r²)
The coefficient of determination, r², is the square of r and represents the proportion of the variance in one variable that is explained by the other through the linear model. For example, an r² of 0.60 means that 60% of the variation in Y can be explained by its linear relationship with X, leaving 40% unexplained.
Related Calculators
Note: This calculator computes the Pearson correlation coefficient for linear relationships only. Correlation does not imply causation, and a low r value does not rule out a non-linear relationship. Verify your data is entered correctly for accurate results.