Correlation Calculator
Calculate Pearson's correlation coefficient (r) between two data sets. Enter paired x and y values.
How to use the correlation calculator
- Enter the x values, separated by commas or spaces.
- Enter the y values in the same order, matching the number of x values.
- The correlation coefficient (r) updates automatically.
What is Pearson's correlation coefficient?
Pearson's correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. The value ranges from −1 to 1: r = 1 means a perfect positive relationship (as one increases, the other increases proportionally), r = −1 means a perfect negative relationship, and r = 0 means no linear relationship.
Worked example: for x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 5 the means are 3 and 4. The sum of the products of the deviations is 6, while the sums of squares are 10 and 6, giving r = 6 ÷ √(10 × 6) = 0.77. That is a strong positive relationship, but well short of 1.00 — y rises steadily apart from one dip from 5 to 4, and that single break alone pulls the coefficient down by almost a quarter of a point.
Frequently asked questions
What counts as a "strong" correlation?
There's no absolute threshold, but a common rule of thumb is: |r| above 0.7 is considered strong, 0.3–0.7 moderate, and below 0.3 weak. Context (field, amount of data) also matters.
Does correlation mean there's a causal relationship?
No — "correlation is not causation" is a fundamental principle in statistics. Two variables can correlate strongly without one causing the other, for example if both are influenced by a common underlying factor.
Does Pearson's r capture all types of relationships?
No, Pearson's r only measures linear relationships. Two variables can have a strong, non-linear relationship (e.g. a U-shaped curve) and still get a low Pearson correlation close to 0.