Pearson R Calculator
Enter paired values using commas, spaces, or new lines. Results appear above this form after submission.
Example Data Table
| Pair | Study Hours | Exam Score |
|---|---|---|
| 1 | 12 | 30 |
| 2 | 15 | 34 |
| 3 | 18 | 36 |
| 4 | 20 | 40 |
| 5 | 22 | 42 |
| 6 | 25 | 47 |
Formula Used
Pearson r measures linear association between two numeric variables. Values near +1 show a strong positive pattern. Values near −1 show a strong negative pattern. Values near 0 suggest weak linear association.
The calculator also estimates covariance, coefficient of determination, simple linear regression slope and intercept, a t statistic for significance, a two tailed p value, and a confidence interval using the Fisher z transformation.
How to Use This Calculator
- Enter X values in the first field.
- Enter matching Y values in the second field.
- Keep both series the same length.
- Choose the desired confidence level.
- Press the calculate button.
- Review the result panel above the form.
- Export your paired data to CSV if needed.
- Use the PDF button to save the full report page.
Frequently Asked Questions
1. What does Pearson r measure?
Pearson r measures the strength and direction of a linear relationship between two numeric variables. It does not confirm causation.
2. What range can Pearson r take?
The coefficient ranges from −1 to +1. Values close to either extreme indicate stronger linear association. Values near zero indicate weaker linear association.
3. Why do both series need equal lengths?
Each X value must match one Y value as a pair. Unequal lengths break the pairing and make correlation invalid.
4. Can Pearson r detect nonlinear patterns?
Not reliably. A curved relationship may produce a low Pearson r even when variables are strongly related in a nonlinear way.
5. What does the p value mean here?
The p value tests whether the observed correlation could appear by chance if the true population correlation were zero.
6. What is r squared?
r squared is the coefficient of determination. It shows the proportion of variance in Y explained by a linear relationship with X.
7. Can outliers change the result?
Yes. Pearson r is sensitive to extreme values. One unusual point can noticeably raise or lower the correlation.
8. When should I avoid Pearson r?
Avoid it when data are ordinal, heavily skewed, strongly nonlinear, or dominated by outliers. Spearman correlation may be better then.