Enter the same number of values in each box — one per line, or separated by commas or spaces.
About this tool
The Correlation Coefficient Calculator measures how strongly two variables move together using Pearson's r. Paste your X values in the first box and the matching Y values in the second, one number per line (or separated by commas, spaces or semicolons); the calculation runs locally in your browser and nothing is sent anywhere.
After finding the means x̄ and ȳ, it computes Sxx = Σ(x − x̄)², Syy = Σ(y − ȳ)² and Sxy = Σ(x − x̄)(y − ȳ). Pearson's r = Sxy / √(Sxx·Syy) always lies between −1 and +1; r² is its square, and the sample covariance is Sxy / (n − 1). A label describes the strength from |r| (≥0.9 very strong, ≥0.7 strong, ≥0.5 moderate, ≥0.3 weak, otherwise negligible) together with the direction.
The two lists must contain the same number of values, and you need at least two pairs. If the lengths differ the tool tells you so rather than guessing which values pair up.
Frequently asked questions
What is Pearson's r?
It is the standardised measure of linear association: r = Sxy / √(Sxx·Syy). It ranges from −1 (perfect negative) through 0 (none) to +1 (perfect positive linear relationship).
How is the strength label decided?
From the absolute value of r: 0.9 and above is very strong, 0.7–0.9 strong, 0.5–0.7 moderate, 0.3–0.5 weak, and below 0.3 negligible. The sign of r gives the positive or negative direction.
Why must both lists be the same length?
Correlation compares paired observations, so each X must have exactly one matching Y. If the counts differ the pairing is ambiguous and the tool reports a length mismatch instead of computing.
Does correlation mean causation?
No. A high r only means the two variables tend to change together; it does not prove one causes the other. A hidden third factor or coincidence can produce strong correlation.
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