Correlation Coefficient Calculator

The Pearson correlation r is the sum of the products of the paired deviations from each mean, divided by the square root of the product of each variable's sum of squared deviations. In short, r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² · Σ(y − ȳ)²).

r ranges from −1 to +1. Values near +1 mean a strong positive linear relationship, near −1 a strong negative one, and near 0 little or no linear relationship. The sign tells you the direction and the magnitude tells you the strength.

A common rough guide: |r| above 0.7 is strong, 0.4 to 0.7 is moderate, and below 0.4 is weak. These cutoffs are conventions, not rules — what counts as strong depends heavily on the field.

r² is the square of the correlation coefficient. It is the fraction of the variation in one variable that is explained by a straight-line relationship with the other. An r of 0.8 means r² = 0.64, so 64% of the variation is explained.

No. A high correlation only shows that two variables move together; it does not prove one causes the other. A hidden third factor or pure coincidence can produce strong correlations between unrelated things.

You need two lists of numbers of equal length, where each pair (x, y) belongs to the same observation. Enter the x values and the y values in the same order so the calculator can pair them correctly.