Correlation Coefficient Calculator (Pearson r)
Enter paired X and Y values to measure how strongly they move together.
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Correlation Coefficient Calculator (Pearson r) by TheCalcTools
How the Correlation Coefficient Calculator (Pearson r) works
Pearson’s r measures the strength of a straight-line relationship between two variables, from −1 (perfect negative) through 0 (none) to +1 (perfect positive).
It is the covariance of X and Y divided by the product of their standard deviations. r² is the share of the variation in Y that a straight line through X explains.
The strength labels used here (0.3, 0.5, 0.7, 0.9) are common rules of thumb; fields differ in what they call strong.
The formula
Worked example
Using the default values shown in the calculator:
| X values | 1, 2, 3, 4, 5, 6 |
|---|---|
| Y values (same order) | 2.1, 3.9, 6.2, 7.8, 10.1, 12.2 |
- The six pairs rise together almost perfectly.
- r = 0.9991, so r² = 0.9982: the straight line explains about 1.00 of the variation in Y.
Result:
| Correlation coefficient r | 0.9991 |
|---|---|
| Coefficient of determination r² | 0.9982 |
| Strength | Very strong positive |
| Sample covariance | 7.0700 |
| Pairs | 6 |
Frequently asked questions
Does correlation mean causation?
No. Two variables can move together because a third factor drives both, or by coincidence. Correlation is evidence of a relationship, not of what causes it.
What if the relationship is curved?
Pearson’s r only captures straight-line relationships. A strong curved pattern can give a low r. Plot the data first.
Sources and further reading
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