Correlation Coefficient Calculator
Calculate Pearson correlation between two variables, with significance testing.
What the Correlation Coefficient Calculator does
The Pearson correlation coefficient measures the strength and direction of a linear relationship, running from −1 to +1. Its square, r², gives the proportion of variance in one variable explained by the other.
Formula
r = Σ((x − x̄)(y − ȳ)) ÷ √(Σ(x − x̄)² × Σ(y − ȳ)²)r² = Coefficient of determinationt = r × √((n − 2) ÷ (1 − r²))
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| X values | text | Yes | Separate values with commas, spaces or new lines. |
| Y values | text | Yes | Separate values with commas, spaces or new lines. |
How to use it
- Enter X values and Y values.
- Select Calculate.
Worked example
X values 1–5 against Y values 2.1, 4.3, 6.2, 8.1, 9.8.
- X
- 1, 2, 3, 4, 5
- Y
- 2.1, 4.3, 6.2, 8.1, 9.8
r ≈ 0.9990, r² ≈ 0.9979 — an almost perfect positive linear relationship.
Frequently asked questions
What does a negative correlation mean?
That the variables move in opposite directions — as one rises, the other tends to fall. The strength depends on the absolute value, not the sign.
Is a significant correlation meaningful?
Statistical significance only says the correlation is unlikely to be zero. With a large enough sample, trivially small correlations become significant without being important.