Correlation Coefficient Calculator: Pearson r, r² and Significance
Enter paired X and Y values. You get Pearson’s r, how strong the link is, r², a p-value for “no correlation” and a scatter plot.
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Correlation r
0.9925
Strong positive- r² (coefficient of determination)
- 0.985
- Pairs n
- 6
- t statistic
- 16.2215
- p-value (two-tailed)
- 0.000085
Correlation shows association, not cause and effect.
Show working
- x̄ = 7, ȳ = 69.5
- Sxx = Σ(x − x̄)² = 70
- Syy = Σ(y − ȳ)² = 633.5
- Sxy = Σ(x − x̄)(y − ȳ) = 209
- r = Sxy / √(Sxx·Syy) = 209 / √(70 × 633.5) = 0.992485
- t = r·√((n − 2)/(1 − r²)) = 16.2215, df = 4
How to use
- Enter the X values in the first box.
- Enter the matching Y values in the same order in the second box.
- Read r, its strength, r² and the p-value.
Good to know
Formula: r = Sxy / √(Sxx·Syy), with Sxy = Σ(x − x̄)(y − ȳ). r runs from −1 (perfect negative straight-line link) through 0 (no straight-line link) to +1 (perfect positive).
Rough guide used for the label: |r| ≥ 0.7 strong, 0.4–0.7 moderate, 0.1–0.4 weak, below 0.1 none. The p-value tests r = 0 with t = r√((n − 2)/(1 − r²)) on n − 2 degrees of freedom.
Correlation is not causation: ice-cream sales and drowning both rise in summer. r also only measures straight-line relationships; a perfect curve can have r near 0, so look at the scatter plot.
Questions
What does r = 0.99 mean?
A very strong positive straight-line relationship: as X goes up, Y almost always goes up in proportion.
What is r²?
The share of the variation in Y explained by a straight line in X. r = 0.9 gives r² = 0.81, or 81%.
What does the p-value tell me?
How likely a correlation this strong would be by chance if there were really none. Below 0.05 is usually called significant.
Is this the same as Spearman’s rank correlation?
No. This is Pearson’s r on the actual values. Spearman’s uses ranks; you can apply this tool to ranks to get it (when there are no ties).
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.