Correlation Calculator
Calculate Pearson correlation coefficient (r), r², Spearman rank correlation, p-value, confidence interval, and regression equation from X and Y data sets.
Pearson r
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r² (Coefficient of Determination) —
Interpretation —
Extended More scenarios, charts & detailed breakdown ▾
Pearson r
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r² —
Sample Size —
Professional Full parameters & maximum detail ▾
Correlation Statistics
Pearson r —
Standard Error of r —
p-value (approx) —
Confidence Interval
95% CI Lower —
95% CI Upper —
Regression
Regression Equation —
Predicted Y —
How to Use This Calculator
- Enter X values as comma-separated numbers (e.g., 1,2,3,4,5).
- Enter matching Y values in the same order.
- Click Calculate to get Pearson r, r², and an interpretation.
- Use the Spearman Rank tab for ordinal data.
- The Professional tab adds p-value, standard error, 95% CI, and regression equation.
Formula
Pearson r = Σ[(xᵢ−x̄)(yᵢ−ȳ)] / √[Σ(xᵢ−x̄)²·Σ(yᵢ−ȳ)²]
Spearman rₛ = 1 − 6Σd² / n(n²−1) where d = rank difference
Example
X: 1,2,3,4,5 | Y: 2,4,5,4,5 → r ≈ 0.9, r² ≈ 0.81 (strong positive correlation).
Frequently Asked Questions
- Pearson r measures the linear relationship between two variables, ranging from −1 (perfect negative) to +1 (perfect positive). A value of 0 indicates no linear relationship.
- |r| ≥ 0.9 = very strong, 0.7–0.9 = strong, 0.5–0.7 = moderate, 0.3–0.5 = weak, < 0.3 = very weak correlation.
- r² tells you the proportion of variance in Y explained by X. If r = 0.8, then r² = 0.64, meaning X explains 64% of the variation in Y.
- Spearman rank correlation (rₛ) measures the monotonic relationship using ranked data. It works for ordinal data and is less sensitive to outliers than Pearson r.
- At least 2 for a basic correlation, but at least 10–20 is recommended for reliable results. More data makes the correlation estimate more stable.