Correlation Calculator
Calculate the Pearson correlation coefficient (r) between two variables. Paste your X and Y values — separately or as pairs — and get r, r², and an honest interpretation of the strength, with the formula worked through.
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Frequently Asked Questions
- What is the Pearson correlation coefficient?
- Pearson's r measures the strength and direction of the linear relationship between two variables. It ranges from −1 (perfect negative correlation) through 0 (no linear relationship) to +1 (perfect positive correlation). It is computed as the sum of the products of each pair's deviations from their means, divided by the square root of the product of the summed squared deviations.
- How do I interpret the strength of a correlation?
- A common rule of thumb, used by this calculator: |r| of 0.7 or above is strong, 0.4 to 0.69 is moderate, 0.1 to 0.39 is weak, and below 0.1 is negligible. These bands are conventions, not laws — what counts as a meaningful correlation depends on your field.
- What does r² tell me?
- r² (the coefficient of determination) is the proportion of the variance in one variable that is linearly associated with the other. An r of 0.8 gives r² = 0.64, meaning 64% of the variation is shared between the two variables.
- Does correlation mean one variable causes the other?
- No. Correlation is not causation. Two variables can be strongly correlated because one causes the other, because both are driven by a third factor, or by pure coincidence. A correlation coefficient alone can never establish a causal link.
- Why might Pearson's r miss a real relationship?
- Pearson's r only measures linear relationships. A perfect U-shaped or other curved relationship can produce an r near zero. It is also sensitive to outliers — a single extreme pair can inflate or destroy the coefficient. Always plot your data as well.
- How many data pairs do I need?
- The calculator requires at least 3 pairs, and the X and Y lists must contain the same number of values. Statistically, correlations from very small samples are unstable — with only a handful of pairs, even a large r can easily arise by chance.