Correlation Coefficient Calculator
Correlation Coefficient Calculator
Enter two paired lists of numbers (matching each x value with its corresponding y value, in order). This calculates Pearson's correlation coefficient (r), the coefficient of determination (r²), and a plain-language read on the strength and direction of the relationship.
r ranges from −1 (a perfect negative relationship, where one variable rises exactly as the other falls) through 0 (no linear relationship at all) up to +1 (a perfect positive relationship) — and it's worth repeating the classic caution that correlation is not causation: a strong r shows two variables tend to move together, but doesn't by itself prove one causes the other, since both could be driven by a shared third factor. This calculator also only measures linear relationships specifically, so two variables with a strong curved (non-linear) relationship can still show a surprisingly low r despite being closely related in a different way.
- Range and meaning: r ranges from −1 (perfect negative relationship) through 0 (no linear relationship) to +1 (perfect positive relationship).
- Correlation is not causation: a strong correlation shows the two variables tend to move together, but doesn't by itself prove that one causes the other.
- Only measures linear relationships: two variables can have a strong non-linear pattern (like a U-shape) and still produce a low Pearson r, since this method specifically detects straight-line trends.
What does r² add beyond r itself?
R² (r squared) represents the proportion of variance in one variable that's explained by the other — an r of 0.8 gives an r² of 0.64, meaning 64% of the variation is explained by the linear relationship.
What counts as a "strong" correlation?
Common rules of thumb treat |r| ≥ 0.7 as strong, 0.3–0.7 as moderate, and below 0.3 as weak — though what counts as meaningful can vary by field (a 0.3 correlation might be notable in social science but weak in physics).
Correlation Coefficient Calculator
Enter two paired lists of numbers (matching each x value with its corresponding y value, in order). This calculates Pearson's correlation coefficient (r), the coefficient of determination (r²), and a plain-language read on the strength and direction of the relationship.
r ranges from −1 (a perfect negative relationship, where one variable rises exactly as the other falls) through 0 (no linear relationship at all) up to +1 (a perfect positive relationship) — and it's worth repeating the classic caution that correlation is not causation: a strong r shows two variables tend to move together, but doesn't by itself prove one causes the other, since both could be driven by a shared third factor. This calculator also only measures linear relationships specifically, so two variables with a strong curved (non-linear) relationship can still show a surprisingly low r despite being closely related in a different way.
- Range and meaning: r ranges from −1 (perfect negative relationship) through 0 (no linear relationship) to +1 (perfect positive relationship).
- Correlation is not causation: a strong correlation shows the two variables tend to move together, but doesn't by itself prove that one causes the other.
- Only measures linear relationships: two variables can have a strong non-linear pattern (like a U-shape) and still produce a low Pearson r, since this method specifically detects straight-line trends.
What does r² add beyond r itself?
R² (r squared) represents the proportion of variance in one variable that's explained by the other — an r of 0.8 gives an r² of 0.64, meaning 64% of the variation is explained by the linear relationship.
What counts as a "strong" correlation?
Common rules of thumb treat |r| ≥ 0.7 as strong, 0.3–0.7 as moderate, and below 0.3 as weak — though what counts as meaningful can vary by field (a 0.3 correlation might be notable in social science but weak in physics).