This tool computes the Pearson product-moment correlation coefficient (r) for two paired data series, measuring how strongly they move together in a straight line. It returns r on a scale from −1 to +1, the coefficient of determination r², and a plain-English strength reading. It is built for statistics coursework, research and data analysis where you want to quantify a relationship between two variables.
How it works
Paste two series of numbers; values pair up by position. The tool computes the mean of each series, then applies the Pearson formula — the covariance of the two variables divided by the product of their standard deviations:
r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] ÷ √[Σ(xᵢ − x̄)² · Σ(yᵢ − ȳ)²]
A result near +1 means a strong positive linear relationship, near −1 a strong negative one, and near 0 little or no linear relationship. Squaring r gives r², the proportion of variance in one variable explained by a linear fit to the other.
Example
For x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 5, the calculator returns r ≈ 0.775 and r² ≈ 0.60. That signals a moderately strong positive relationship — as x increases, y tends to increase — with about 60% of y’s variance explained by the linear fit. A perfectly proportional pair like y = 2x would return r = 1.
Paste your two series — every value pairs by position, and all calculation happens in your browser.