Pearson Correlation Calculator
Measuring a Straight-Line Relationship
Pearson's r is the most widely reported correlation statistic in applied statistics, and for good reason: it gives a single number, bounded between −1 and 1, that captures how tightly two variables move together in a linear fashion. It says nothing about curved relationships, and a strong r doesn't establish causation — but as a first diagnostic on paired numeric data, it's hard to beat for speed and interpretability.
The Formula
Significance is tested by converting r to a t statistic: t = r√(df / (1−r²)), with df = n − 2.
Worked Example
x = 1, 2, 3, 4, 5. y = 2, 4, 5, 4, 5.
| Quantity | Value |
|---|---|
| r | 0.7746 |
| df | 3 |
| Interpretation | Strong positive linear relationship |
Computed directly from the calculator's formula.
Interpreting the Strength of r
| |r| range | Strength |
|---|---|
| 0.90 – 1.00 | Very strong |
| 0.70 – 0.89 | Strong |
| 0.50 – 0.69 | Moderate |
| 0.30 – 0.49 | Weak |
| 0.00 – 0.29 | Very weak / negligible |
Bands taken directly from the calculator's classification logic.
Where This Calculation Matters
- Exploratory data analysis — scanning pairs of numeric variables for linear relationships before building a more complex model.
- Feature screening — in predictive modeling, correlation with the target variable is often the first filter applied to a large set of candidate predictors.
- Validating instrument agreement — checking whether two measurement methods (e.g., two thermometers or two lab assays) track each other closely.
How to Use This Calculator
- Enter the X values as a comma-separated list.
- Enter the Y values as a comma-separated list, in the same order (at least 3 paired values).
- Select Calculate to get r, the significance test, and the strength interpretation.
Related Calculations
For rank-based data or non-linear monotonic relationships, use the Spearman Rank Correlation Calculator. To fit a predictive line through the same data, see the Linear Regression Calculator.