Calculate Pearson's r in Seconds
Enter two equal-length datasets (X and Y). Use commas, spaces, or new lines between numbers.
What Is the Pearson Correlation Coefficient?
The Pearson correlation coefficient (usually written as r) measures the strength and direction of a linear relationship between two numeric variables. It ranges from -1 to +1:
- +1: perfect positive linear relationship
- 0: no linear relationship
- -1: perfect negative linear relationship
This statistic is widely used in statistics, data science, finance, psychology, education, and research methods whenever you want to understand whether two variables move together.
How to Use This Pearson Correlation Calculator
Step-by-step
- Paste your first dataset into the X values box.
- Paste your second dataset into the Y values box.
- Click Calculate Correlation.
- Read the resulting r value, direction, and strength interpretation.
You can also click Load Sample Data to test how the calculator works.
Pearson Correlation Formula
The calculator uses the standard computational formula:
Where:
- n = number of paired observations
- Σxy = sum of products of paired values
- Σx, Σy = sums of X and Y values
- Σx², Σy² = sums of squared X and Y values
How to Interpret Pearson's r
While interpretation can vary by field, a common rule of thumb for 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
The sign (+ or -) gives the direction. Positive means both variables tend to increase together. Negative means one tends to increase while the other decreases.
Important Notes and Common Mistakes
1) Correlation does not imply causation
Even a high correlation does not prove that X causes Y. A third factor may influence both variables.
2) Pearson captures linear relationships
If the relationship is curved or non-linear, Pearson's r can be misleadingly low even when variables are strongly related.
3) Outliers can distort results
A single extreme point can significantly inflate or reduce the coefficient. Inspect your data visually when possible.
4) Use paired observations
Each X value must correspond to exactly one Y value from the same observation or case.
Pearson vs. Spearman Correlation
Use Pearson correlation when data are numeric, paired, and approximately linear with no severe outliers. Use Spearman rank correlation when your data are ordinal, not normally distributed, or monotonic but not linear.
Quick FAQ
Can Pearson r be greater than 1?
No. Valid values are always between -1 and +1.
What if one variable has no variation?
The correlation is undefined because the denominator becomes zero. This calculator will show an error for that case.
What is r²?
r² is the coefficient of determination. It indicates the proportion of shared linear variance between variables.