Calculating correlation...
Submit paired data to calculate Pearson r
The result will show r, r squared, covariance, a scatter plot, and a step-by-step deviation table.
Pearson r explained
What the correlation coefficient measures
The Pearson correlation coefficient calculator measures the strength and direction of a linear relationship between two numeric variables. Pearson r ranges from -1 to +1: negative values slope downward, positive values slope upward, and values near 0 show little linear association.
The r squared value is r multiplied by itself. It describes the share of variation aligned with the fitted linear relationship in the submitted data, but correlation does not prove causation.
Pearson r formula
Pearson r compares centered x and y movement against their total squared spread.
Correlation scale
The sign gives direction; the distance from 0 gives strength.
Scatter plot patterns
Pearson r is easiest to understand visually: points close to a line produce stronger absolute correlation.
Positive
r > 0
Negative
r < 0
Weak / none
r near 0
Example correlation values
| r value | Direction | Meaning |
|---|---|---|
| 0.95 | Positive | Near-perfect upward linear association |
| -0.82 | Negative | Very strong downward linear association |
| 0.28 | Positive | Weak upward linear association |
| 0.02 | Near zero | Little or no linear association |
FAQ
What is Pearson r?
Pearson r is a number from -1 to +1 that describes the direction and strength of a linear relationship between two numeric variables.
What is r squared?
R squared is r multiplied by itself. It is often read as the share of variation aligned with a linear relationship in the data.
Does correlation prove causation?
No. Pearson correlation can identify association, but study design and domain evidence are needed before making causal claims.
External references