We use cookies.This website uses essential cookies to operate core features. With your consent, we also use analytics cookies to understand traffic and improve the service. For more details, see our .
We use cookies.This website uses essential cookies to operate core features. With your consent, we also use analytics cookies to understand traffic and improve the service. For more details, see our .
If this tool helped you, you can buy us a coffee ☕
Input two sets of continuous data, quickly calculate Pearson correlation coefficient R, and determine the strength of linear correlation.
The number of data points for X and Y must be equal and correspond one-to-one. Each set requires at least 2 numbers (at least 3 for significance testing). Supports separation by commas, spaces, newlines, or semicolons. Non-numeric content will be ignored.
Enter paired X and Y data to view the correlation coefficient.
Here is a look at who commonly uses this tool:
The Pearson correlation coefficient (denoted as R) measures the direction and strength of the linear relationship between two continuous variables. The formula is:
R = [ Σ(xᵢ - x̄)(yᵢ - ȳ) ] / [ √(Σ(xᵢ - x̄)²) · √(Σ(yᵢ - ȳ)²) ]
Where x̄ is the mean of the X variable and ȳ is the mean of the Y variable. The numerator is the covariance, and the denominator is the product of their respective standard deviations. Simply put: the more the directions in which X and Y deviate from their means "sync up," the larger the numerator, and the closer R gets to 1 or -1. If the directions are completely random, the numerator approaches 0, and R approaches 0.
Suppose we have 5 students, and their weekly "Study Time (hours)" and "Mock Exam Scores (out of 100)" are as follows:
Study Time (X): 2, 4, 6, 8, 10
Exam Score (Y): 55, 60, 70, 80, 85
Enter the following sequentially into the X box of the calculator:
2
4
6
8
10
Enter the following sequentially into the Y box:
55
60
70
80
85
After clicking calculate, the tool will output R = 0.9923. Let's manually verify this:
Result Interpretation: R=0.99 is very close to 1, indicating an almost perfect positive linear correlation between study time and exam scores—the longer you study, the higher your score.
Control Example: Zero Correlation
X: 1, 2, 3, 4, 5
Y: 10, 15, 8, 12, 20
Entering this yields R ≈ 0.10. Although Y appears to fluctuate, it has no linear relationship with the changes in X. An R value close to 0 indicates that these two variables are uncorrelated (or non-linear).
Extreme Perfect Negative Correlation
X: 10, 20, 30, 40
Y: 90, 70, 50, 30
Entering this yields R = -1.00, a strict negative linear correlation: as X increases, Y decreases proportionally.
| Absolute Value of R | Correlation Strength | Description |
|---|---|---|
| 0.00 – 0.19 | Very weak or no linear correlation | Almost no linear relationship exists between the two variables; other forms (like curves) may need to be considered. |
| 0.20 – 0.39 | Weak correlation | Some linear trend exists, but predictive power is limited. |
| 0.40 – 0.69 | Moderate correlation | A relatively obvious linear relationship, can be used for rough estimation. |
| 0.70 – 0.89 | Strong correlation | Strong linear relationship; variables significantly influence each other. |
| 0.90 – 1.00 | Very strong correlation | Can almost be considered a linear functional relationship. |
Note: The positive or negative sign of R indicates the direction, while the absolute value determines the strength. If R is negative and its absolute value is large, it indicates a strong inverse correlation.
