Correlation Coefficient Calculator
Pearson correlation coefficient (r) quantifies the strength and direction of linear relationship between two variables. Enter two paired datasets (X and Y values). The calculator computes Pearson r, R-squared, and interpretation. Correlation ranges from -1 (perfect negative) to 1 (perfect positive), with 0 indicating no linear relationship. This is fundamental in exploratory data analysis, research, and understanding relationships between variables.
Pearson correlation formula
r = [n*Σ(xy) - Σ(x)*Σ(y)] / sqrt([n*Σ(x²)-(Σ(x))²]*[n*Σ(y²)-(Σ(y))²])
R² = r²
Where n is the number of pairs
Correlation strength interpretation
- 0.90 to 1.00: Very strong positive. (0.90 to -1.00 for negative)
- 0.70 to 0.90: Strong positive.
- 0.50 to 0.70: Moderate positive.
- 0.30 to 0.50: Weak positive.
- 0.00 to 0.30: Very weak or no relationship.
Correlation: frequently asked questions
What is Pearson correlation coefficient?
Pearson r measures the linear relationship between two variables, ranging from -1 to 1. r = 1 means perfect positive correlation, r = -1 means perfect negative correlation, r = 0 means no linear relationship.
How do I interpret the correlation coefficient?
Absolute value 0-0.3: weak. 0.3-0.7: moderate. 0.7-1.0: strong. Sign indicates direction: positive (both increase together) or negative (one increases as the other decreases).
What is R-squared?
R-squared (r^2) is the coefficient of determination, the proportion of variance in one variable explained by the other. If r = 0.7, then r^2 = 0.49, meaning 49% of variance is explained.
Does correlation imply causation?
No. Correlation measures linear association only. Two variables can be correlated without one causing the other. A third variable might influence both.
What is the difference between correlation and regression?
Correlation measures the strength of the relationship. Regression predicts one variable from another. Both use the same underlying data but answer different questions.
Official sources
- NIST/SEMATECH e-Handbook: NIST Handbook.
- American Statistical Association: ASA.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.