The Pearson product moment correlation coefficient (PMCC, or simply Pearson r) is calculated from paired (x, y) data. It standardizes the covariance between x and y by the product of their standard deviations, producing a value always between -1 and +1.
The formula can also be written as: r = covariance(x, y) / (std_dev(x) * std_dev(y)). Both forms produce identical results. This is why r is scale-independent: multiplying x or y by any constant does not change r. Descriptive statistics for each variable (mean, standard deviation) are computed separately; the Mean Median Mode Calculator computes those individual measures for any data set.
Excel has two built-in functions that calculate the Pearson correlation coefficient. Both return identical results for the same input data.
| Task | Excel | This Calculator |
|---|---|---|
| Pearson r | =CORREL(x_range, y_range) | Enter x and y, click Calculate |
| R-squared | =CORREL(...)^2 | Shown automatically |
| Interpretation label | Manual lookup required | Shown automatically |
| Step-by-step workings | Not available | Shown in results card |
| Batch multiple pairs | Yes (drag formula) | One calculation at a time |
For a one-time calculation with step-by-step intermediate values, this calculator is faster than setting up Excel. For batch calculations across many variable pairs in a dataset, Excel or Python pandas are better suited. Correlation is closely related to linear interpolation between paired data points; the Linear Interpolation Calculator estimates unknown values along a line defined by two points.
The correlation coefficient r is always between -1 and +1. Both extreme values represent perfect linear relationships; intermediate values describe the degree of scatter around that line. The sign indicates direction; the magnitude indicates strength.
| r value | Interpretation | What it means | Real-world example |
|---|---|---|---|
| +1.0 | Perfect positive | Every point on a line, upward | Temperature in C vs F |
| +0.9 to +1.0 | Very strong positive | Nearly all variance explained | Height vs arm span |
| +0.7 to +0.9 | Strong positive | Clear upward trend | Advertising spend vs sales |
| +0.5 to +0.7 | Moderate positive | Visible trend, notable scatter | Study hours vs test score |
| +0.3 to +0.5 | Weak positive | Slight upward tendency | Exercise vs mood |
| 0.0 to +0.3 | Very weak / none | Essentially unrelated linearly | Shoe size vs IQ |
| Negative | Same strengths, downward | As x increases, y decreases | Speed vs fuel economy |
Important: r = 0 does not mean the variables are unrelated. It means no linear relationship exists. A strong U-shaped or exponential relationship can produce r = 0 while the variables are clearly associated. Always visualize the data alongside any r value. For estimating values within a data range, see the Interpolation Calculator.
X: 2, 4, 5, 7, 8, 10 and Y: 3, 5, 6, 8, 9, 12. Find the Pearson correlation coefficient.
Researches and verifies the formulas, methodology, and source data behind each calculator on CalculatorFlux. All tools are built and checked against the cited references before publication.