Correlation Coefficient Calculator
Calculate Pearson correlation coefficient to measure linear relationship between two variables
Enter Your Data Sets
Input two sets of numerical data (must have equal length)
5 values
5 values
Interpretation Guide
0.9 to 1.0 (or -0.9 to -1.0)Very Strong
0.7 to 0.9 (or -0.7 to -0.9)Strong
0.5 to 0.7 (or -0.5 to -0.7)Moderate
0.3 to 0.5 (or -0.3 to -0.5)Weak
0.0 to 0.3 (or 0.0 to -0.3)Very Weak/None
Positive values indicate positive relationship, negative values indicate inverse relationship
Correlation
0.7746
StrongPositive
R-Squared (R²)0.6000
Sample Size (n)5
X Mean3.0000
Y Mean4.0000
Formula
r = Σ[(x-x̄)(y-ȳ)] / √[Σ(x-x̄)²·Σ(y-ȳ)²]
Pearson correlation coefficient (r) ranges from -1 to +1
What It Means
There is a strong positive linear relationship between X and Y.
R² = 60.0% of variance in Y is explained by X
Understanding Correlation
The correlation coefficient measures the strength and direction of a linear relationship between two variables. It's one of the most important statistical concepts for understanding relationships in data.
Key Concepts
- Range: Correlation always falls between -1 and +1
- +1: Perfect positive correlation (as X increases, Y increases proportionally)
- -1: Perfect negative correlation (as X increases, Y decreases proportionally)
- 0: No linear correlation (no linear relationship)
Important Notes
- • Correlation ≠ Causation (relationship doesn't imply cause and effect)
- • Only measures LINEAR relationships
- • Sensitive to outliers
- • Requires at least 3 data pairs, ideally 30+ for reliability