Pearson r Calculator
Enter two equal-length sets of numbers to compute the Pearson correlation coefficient (r), r², and trend details.
What is the r correlation coefficient?
The Pearson correlation coefficient, usually written as r, measures the strength and direction of a linear relationship between two variables. Values range from -1 to +1.
- r = +1: perfect positive linear relationship
- r = 0: no linear relationship
- r = -1: perfect negative linear relationship
If one variable tends to increase when the other increases, correlation is positive. If one increases while the other decreases, correlation is negative.
Pearson correlation formula
This calculator uses the standard Pearson product-moment correlation equation:
In plain language, it compares how paired values co-vary (move together) relative to the total spread in each variable.
How to use this r correlation calculator
Step 1: Add paired data
Enter your first list in the X field and the second list in the Y field. Each X value should correspond to one Y value from the same row or case.
Step 2: Click “Calculate r”
The tool instantly returns:
- Pearson r
- Coefficient of determination (r²)
- Direction and strength interpretation
- Means, regression slope, and intercept
Step 3: Interpret with context
Statistical output is most useful when interpreted alongside domain knowledge. In education, health, finance, and behavioral data, “strong” or “weak” can depend on measurement noise and sample size.
How to interpret r values
A common guideline based on absolute value |r| is:
- 0.00 to 0.09: negligible
- 0.10 to 0.29: weak
- 0.30 to 0.49: moderate
- 0.50 to 0.69: strong
- 0.70 to 0.89: very strong
- 0.90 to 1.00: nearly perfect
These cutoffs are rules of thumb, not universal laws.
Important caveats
Correlation is not causation
A high correlation does not prove that X causes Y. A third variable (confounder), reverse causality, or coincidence can produce similar patterns.
Pearson r detects linear relationships
If your relationship is curved or nonlinear, Pearson r may be low even when a clear association exists. Consider scatter plots and nonlinear models.
Outliers can distort results
One extreme data point can strongly inflate or suppress r. Always inspect your data visually before drawing conclusions.
Related statistics you might need
- Covariance: raw co-movement (scale-dependent)
- Spearman rank correlation: robust for monotonic/non-normal data
- Linear regression slope: expected Y change per unit X
- r²: proportion of variance in Y explained by linear X relationship
Quick example
Suppose you track study hours and exam scores for 8 students. If r = 0.82, that indicates a very strong positive linear relationship: students who study more generally score higher. If r² = 0.67, then about 67% of score variation is linearly associated with study time in this sample.
Final notes
Use this Pearson correlation calculator as a fast, transparent tool for exploratory data analysis, statistics homework, research prep, and quality checks. For publication-level inference, combine this with confidence intervals, p-values, and diagnostics.