Correlation Coefficient Calculator
Pearson's r, r², and the line — with the caveats.
Work out Correlation Coefficient. Pearson's r, r², and the line — with the caveats. Free, with no account and nothing to install.
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Pearson's r
0.9512
Very strong positive · r² = 0.9048 · p = 0.0003
Pearson's r measures linear association only, on a scale from −1 to 1. A perfect parabola has an r near zero, which says nothing about whether the relationship is strong — only that it is not a straight line. Plot the data before trusting any correlation coefficient. r² is the share of variance in one variable that the linear relationship accounts for. An r of 0.7 sounds substantial and explains less than half the variation, which is why r² is the more honest figure to quote. Correlation does not establish causation, and the reasons are worth naming: the arrow may run the other way, a third variable may drive both, or the pattern may be a coincidence in a small sample. The p-value tests only whether r differs from zero — not whether the relationship means anything.
How the Correlation Coefficient Calculator works
Pearson's r from paired data, with r², the best-fit line and the significance test that belongs with it. r measures straight-line association only — a perfect parabola has an r near zero.
Also known as: calculate pearson r · how correlated are these · r squared from data · does correlation mean causation
Frequently asked questions
What does Pearson's r measure?
Linear association, on a scale from −1 to 1. It measures how close the points lie to a straight line and nothing else, which is why plotting the data first is not optional.
What is r² and why does it matter more?
The share of variance in one variable that the linear relationship accounts for. An r of 0.7 sounds substantial and explains less than half the variation — r² is the more honest figure to quote.
Does correlation imply causation?
No. The arrow may run the other way, a third variable may drive both, or the pattern may be coincidence in a small sample. The p-value tests only whether r differs from zero, not whether the relationship means anything.
What counts as a strong correlation?
It depends entirely on the field. 0.7 is weak in physics and remarkable in psychology. The bands here are a rough guide and no substitute for knowing what is typical in your area.
Can r be misleading?
Very. Anscombe's quartet is four datasets with identical r, means and regression lines that look nothing alike when plotted — one is a clean line, one a curve, one has a single outlier driving everything.
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