This free Correlation Coefficient Calculator computes both Pearson’s r and Spearman’s rank correlation (ρ) from your data. Enter paired values or separate X and Y lists to instantly calculate the correlation coefficient, strength, direction, R², and p-value, with step-by-step working.
A correlation coefficient measures the strength and direction of a relationship between two variables.
$$ r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})} {\sqrt{\sum (x_i - \bar{x})^2 \; \sum (y_i - \bar{y})^2}} $$
$$ \rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} $$
Data pairs: (1,2), (2,3), (3,3.5), (4,5), (5,7)
$$ r = 0.991 \;\;\Rightarrow\;\; \text{very strong positive correlation} $$
Same dataset ranked: X = [1, 2, 3, 4, 5], Y ranks = [1, 2, 3, 4, 5]
$$ \rho = 1.0 \;\;\Rightarrow\;\; \text{perfect monotonic relationship} $$
Q: What’s the difference between Pearson and Spearman correlation?
A: Pearson measures linear relationships using raw values, while Spearman measures monotonic relationships using ranked values.
Q: Can correlation imply causation?
A: No. Correlation only shows association, not cause-and-effect.
Q: What does R² mean?
A: It represents the proportion of variance in Y explained by X.
Q: What is a good correlation coefficient?
A: It depends on context, but |r| above 0.5 is often considered strong.