Correlation Coefficient Calculator
Calculate Pearson r to measure linear correlation strength.
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Enter paired X and Y values, each separated by commas or spaces. Both must have the same count. The calculator computes Pearson's r (ranging from -1 to 1), R-squared (the proportion of variance explained), and provides a plain-language interpretation of the correlation strength.
About the Pearson Correlation Coefficient
Pearson's r measures the strength and direction of a linear relationship between two variables. A value of 1 means perfect positive linear correlation, -1 means perfect negative, and 0 means no linear correlation. R-squared tells you what percentage of the variability in Y is explained by X. It is the most widely used correlation measure in statistics, research, and data science.
Frequently Asked Questions
What is a strong correlation?
Generally, |r| >= 0.7 is strong, 0.5-0.7 is moderate, 0.3-0.5 is weak, and below 0.3 is very weak. Context matters: in some fields like physics, r = 0.9 is expected, while in social science, r = 0.3 may be notable.
Does correlation imply causation?
No. Correlation measures association, not causation. Two variables can be correlated due to a third confounding variable. Establishing causation requires controlled experiments or careful causal inference methods.
When should I use Spearman instead of Pearson?
Use Spearman rank correlation when the relationship is monotonic but not linear, when data is ordinal, or when there are significant outliers. Spearman is based on ranks and is more robust to non-normality.