Correlation Calculator
Do Two Variables Move Together?
The Pearson correlation coefficient measures how closely two variables track a straight-line relationship — not whether one causes the other, only whether they tend to rise and fall together. It's bounded between −1 and +1, which makes it one of the easiest statistics to interpret at a glance once you know what the endpoints and midpoints mean.
The Formula
The numerator captures how x and y vary together (their covariance); the denominator normalizes by how much each varies on its own, which is what keeps r confined to the −1 to +1 range regardless of the original units.
Interpreting the Strength of r
| |r| range | Interpretation |
|---|---|
| 0.00 – 0.29 | Weak |
| 0.30 – 0.69 | Moderate |
| 0.70 – 1.00 | Strong |
Worked example: for x = 1,2,3,4,5,6,7,8 and y = 2,4,5,4,5,7,8,9, r = 0.951 (r² = 0.905) — a strong positive relationship, meaning roughly 90% of the variation in y lines up with a linear trend in x.
Where This Matters
- Finance — correlation between assets is central to portfolio diversification; low or negative correlation reduces overall risk.
- Research and experimentation — quantifying the strength of a relationship between two measured variables before building a more detailed model.
- Quality and process monitoring — checking whether two process measurements move together in ways that suggest a shared cause.
- Feature screening — in data analysis, correlation is a quick first pass for identifying which variables might be worth deeper modeling.
How to Use This Calculator
- Enter your X values, separated by commas.
- Enter your Y values, separated by commas, in the same order as the corresponding X values.
- Select Calculate to get the correlation coefficient r, r², and a significance test.
Related Calculations
To go beyond strength of association and fit an actual predictive equation, use the Regression Calculator. For testing whether two categorical variables are related, see the Chi-Square Calculator.