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Statistics — Association
Correlation Coefficient Calculator
Paste your paired X and Y values to get Pearson’s correlation coefficient r, r-squared and covariance — how strongly two variables move together.
Correlation coefficient (r)
—
Pearson’s r, from −1 to +1.
| Pairs n | — |
|---|---|
| R squared r², shared variance | — |
| Covariance sample | — |
| Mean of X | — |
| Mean of Y | — |
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Enter your figures above to see the step-by-step working.
Correlation is not causation — r measures linear association onlyEverything computed client-side — nothing leaves this page
How the Correlation Coefficient Calculator Works
Pearson’s correlation coefficient, r, measures the strength and direction of the straight-line relationship between two variables. It runs from −1 (a perfect downhill line) through 0 (no linear relationship) to +1 (a perfect uphill line). Paste your paired X and Y values and the desk returns r, its square, and the covariance.
Correlation is not causation, and r only captures linear association — two variables can be strongly related in a curved pattern yet show an r near zero. The r² value tells you the proportion of variance in one variable explained by the other.
r = Σ(x − x̄)(y − ȳ) ÷ √( Σ(x − x̄)² · Σ(y − ȳ)² )
Frequently Asked Questions
What does the correlation coefficient tell me?
It summarises how closely two variables move together in a straight line. Values near +1 or −1 indicate a strong linear relationship; values near 0 indicate little or no linear relationship. The sign shows the direction.
Does a high correlation mean one thing causes the other?
No. Correlation measures association, not causation. A strong r can arise from coincidence, a shared third cause, or reverse causation. Establishing cause needs controlled study design, not just a correlation.
Why do my X and Y need the same number of values?
Correlation is computed on matched pairs, so each X must have a corresponding Y. If the two lists differ in length, the calculator uses the first matched pairs and flags the mismatch.
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