Correlation Coefficient Calculator
Measure the strength and direction of the linear relationship between two variables using up to 4 paired X and Y values.
Only the first this-many X/Y pairs below are used (2 to 4 pairs).
Your results
Calculation breakdown
- Pearson correlation
- r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² × Σ(y − ȳ)²)
Worked example
Comparing hours studied (1, 2, 3, 4) against test scores (2, 4, 5, 8) gives a correlation coefficient close to 0.98, indicating a strong positive relationship.
Assumptions
- Measures only linear relationships; a strong non-linear pattern can still produce a low r value.
- With only 2–4 data pairs the result is illustrative rather than statistically robust.
How this calculator works
Enter up to 4 paired X and Y values to calculate the Pearson correlation coefficient (r), showing how strongly and in what direction the two variables move together, along with the coefficient of determination (r²).
Frequently asked questions
What does r = 1 mean?
An r of 1 means a perfect positive linear relationship — as X increases, Y increases proportionally every time.
Does correlation prove causation?
No, a strong correlation only shows two variables move together; it does not prove one causes the other.
Why is r² shown as well as r?
r² (the coefficient of determination) shows the proportion of variation in Y that is explained by X, which some people find more intuitive than r alone.