Correlation Coefficient Calculator
Calculate Pearson’s product-moment correlation coefficient (r) between two continuous variables to measure the strength and direction of their linear association.
Values for first variable X
Matching values for second variable Y
Bounded between −1.0000 (perfect negative) and +1.0000 (perfect positive)
How to Use This Calculator
- Enter values for variable X.
- Enter matching values for variable Y.
- Inspect Pearson’s r, association strength, and shared variance (R²).
Formula & Calculation Methodology
Pearson’s r divides the covariance of X and Y by the product of their individual standard deviations, normalizing the metric between −1 and +1.
Worked Example
Evaluating X: 10, 20, 30, 40, 50 and Y: 15, 28, 42, 58, 70
Inverse relationship X: 1, 2, 3 and Y: 9, 6, 3
Frequently Asked Questions
What is the scale of Pearson’s correlation coefficient?↓
+1 indicates perfect positive correlation, 0 indicates no linear relationship, and −1 indicates perfect inverse correlation.
Does a correlation of zero mean variables are completely independent?↓
No. Pearson’s r only detects linear relationships. Non-linear relationships (like y = x²) can have an r of 0 despite complete deterministic dependence.
How does Pearson’s r differ from Spearman’s rho?↓
Pearson’s r evaluates raw linear data; Spearman’s rank correlation evaluates monotonic relationships using ranks rather than absolute magnitudes.
What is a limitation of Pearson’s correlation?↓
Pearson’s r is sensitive to extreme outliers, which can artificially inflate or deflate the apparent strength of association.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.