Correlation Calculator (Pearson's r)
Calculate Pearson correlation coefficient to measure the strength and direction of the linear relationship between two variables. Essential for data analysis and research.
Interpreting Correlation Coefficients
Perfect Positive (r = +1.0)
Perfect linear relationship - as X increases, Y increases proportionally
Strong Positive (0.7 < r < 1.0)
Strong tendency for Y to increase as X increases
Moderate Positive (0.4 < r < 0.7)
Moderate tendency for Y to increase as X increases
Weak/No Correlation (-0.4 < r < 0.4)
Little to no linear relationship between variables
Moderate Negative (-0.7 < r < -0.4)
Moderate tendency for Y to decrease as X increases
Strong Negative (-1.0 < r < -0.7)
Strong tendency for Y to decrease as X increases
About r² (R-squared):
The coefficient of determination (r²) shows what percentage of variation in Y can be explained by X. For example, r² = 0.64 means 64% of Y's variation is explained by its linear relationship with X.
Understanding Correlation
What is Pearson Correlation?
Pearson's correlation coefficient (r) measures the strength and direction of a linear relationship between two continuous variables. Values range from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear correlation.
When to Use This Calculator
- Testing if two variables are related (e.g., study hours vs. test scores)
- Analyzing relationships in scientific research
- Financial analysis (e.g., stock price vs. market index)
- Quality control and process improvement
- Validating measurement instruments
Real-World Example
If studying the relationship between hours studied (X) and exam scores (Y) yields r = 0.85, this indicates a strong positive correlation. Students who study more hours tend to score higher, and about 72% (r² = 0.72) of the variation in exam scores can be explained by study time.
Important Limitations
- Correlation ≠ Causation: Strong correlation doesn't prove one variable causes the other
- Linear only: Pearson's r only measures linear relationships, not curved patterns
- Outliers matter: A few extreme values can significantly affect the correlation
- Sample size: Need adequate data points (typically n ≥ 30) for reliable results
Common Mistakes
- Assuming correlation proves causation
- Using Pearson's r with non-linear relationships
- Ignoring outliers that distort results
- Comparing correlations from different sample sizes
Educational Purpose Disclaimer
This calculator is provided for educational purposes only. Results should not be used as the sole basis for critical decisions. Always verify important calculations independently and consult qualified professionals when needed.