Correlation Coefficient Calculator
Find the Pearson correlation coefficient for paired data.
All calculations happen locally in your browser — nothing is uploaded, stored or tracked.
Add paired values
One (x, y) pair per row.
Calculate
Results update as you type.
Interpret r
Closer to ±1 means a stronger linear relationship.
What Is the Correlation Coefficient?
The Pearson correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It always lies between −1 and +1: +1 is a perfect positive relationship, −1 a perfect negative one, and 0 no linear relationship.
The calculator reports r, the coefficient of determination r² (the proportion of variance shared by the two variables), and the sample covariance. It also shows the number of pairs, which matters because small samples produce unreliable correlations.
The Formula
Each pair's deviations from the means are multiplied; the sum is divided by the product of the standard deviations. The sign of r shows direction, the magnitude shows strength.
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Frequently Asked Questions
What does r = 0.8 mean?
A strong positive linear relationship: as x increases, y tends to increase, and about 64% (r²) of the variation in y is explained by x.
What is the difference between correlation and causation?
Correlation measures association only. Two variables can be strongly correlated without one causing the other.
Can r be greater than 1?
No — by construction r is always between −1 and +1. A value outside this range indicates a calculation error.
How many data points do I need?
At least two pairs are required mathematically, but correlations from very small samples are unstable — more data is much more reliable.
What is r²?
The coefficient of determination: the fraction of variance in one variable explained by the linear relationship with the other.