The correlation calculator computes the Pearson correlation coefficient (r) and coefficient of determination (r²) for paired x,y data. Enter pairs to measure the linear relationship strength.
Pearson Correlation Calculator
How to Interpret the Pearson Correlation
Pearson r measures the strength and direction of the linear relationship between two variables. Values range from −1 to +1.
Interpreting r
|r| ≥ 0.9: very strong. 0.7–0.9: strong. 0.5–0.7: moderate. 0.3–0.5: weak. |r| < 0.3: very weak or no linear relationship. r = +1: perfect positive. r = −1: perfect negative. r = 0: no linear correlation (but could have nonlinear relationship).
Coefficient of Determination (r²)
r² × 100% is the percentage of variance in y explained by x. r = 0.8 → r² = 0.64 → x explains 64% of variation in y. The remaining 36% comes from other factors not in the model.
Correlation vs Causation
Correlation doesn't prove causation. Two variables can correlate due to a third hidden variable (confounding). Always think critically about whether a correlation makes theoretical sense before concluding causation.
FAQ
What is Pearson correlation coefficient?
Pearson r measures the linear relationship between two variables. r ranges from −1 (perfect negative correlation) to +1 (perfect positive correlation). r = 0 means no linear relationship. r = 0.9 means strong positive correlation — as x increases, y tends to increase proportionally.
How do you interpret r and r²?
r = 0.7: moderate-strong positive correlation. r = −0.5: moderate negative correlation. r² = coefficient of determination: the proportion of variance in y explained by x. r² = 0.49 means x explains 49% of the variation in y. The other 51% comes from other factors.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
Does correlation imply causation?
No. Two variables can be correlated due to a third confounding variable. Ice cream sales and drowning rates correlate positively — both increase in summer. The causal factor is temperature/season, not ice cream causing drowning. Correlation is a necessary but not sufficient condition for causation.