Correlation Coefficient Calculator
Calculate Pearson’s r, r² and Spearman’s rank correlation for paired data.
Your inputs
Results
Pearson r
0.774597
- r² (coefficient of determination)
- 0.6
- Spearman ρ (rank)
- 0.737865
- Reading
- strong positive linear relationship
✓Exact calculation — rounded only for display
Notes for this result
- Correlation does not imply causation, and Pearson r only measures linear association.
What this calculator does
Correlation measures how strongly two variables move together. Pearson captures linear relationships; Spearman captures monotonic ones using ranks.
Formula and method
r = Σ(x − x̄)(y − ȳ) ÷ √(Σ(x − x̄)² Σ(y − ȳ)²); Spearman ρ = Pearson r of the ranks (ties averaged)
Worked example
Calculated by this tool with its default inputs:
Inputs
- X values: 1, 2, 3, 4, 5
- Y values (same count): 2, 4, 5, 4, 5
Results
- Pearson r: 0.774597
- r² (coefficient of determination): 0.6
- Spearman ρ (rank): 0.737865
- Reading: strong positive linear relationship
How to read the results
r near ±1 is a strong linear relationship; near 0 is weak or none.
Assumptions and limitations
- Correlation does not imply causation.
Questions
When should I use Spearman?
When the relationship is monotonic but not linear, or data are ranks or have outliers.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
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