How to calculate R² from r
The coefficient of determination, written R², is simply the correlation coefficient squared: R² = r². It tells you the proportion of the variation in one variable that is explained by the other. For r = 0.9, R² = 0.9 × 0.9 = 0.81, meaning about 81% of the variance is explained. R squared is literally the square of Pearson’s r, which the correlation coefficient calculator returns.
How to use this calculator
Enter the correlation coefficient r, which must lie between −1 and 1. The result shows R² and the equivalent percentage of variance explained. If you need r itself from raw data, compute it first, then square it here.
Values outside −1 to 1 are rejected, since a correlation cannot exceed a perfect linear fit in either direction. Remember that the remaining share — 19% in the r = 0.9 example — is variation the relationship does not account for, left to other factors and noise. The "variance explained" phrasing only makes sense once you know the total variance, reported by the variance calculator.
Reading R² values
R² ranges from 0 to 1. A value near 1 means the model explains almost all the variation, while a value near 0 means it explains very little. Because it is squared, a strong negative correlation (r = −0.9) gives the same R² = 0.81 as a strong positive one. R² measures explained variance but not cause and effect. For asymmetry of a distribution instead, see the skewness calculator.
Frequently asked questions
- How do I calculate the coefficient of determination?
- Square the correlation coefficient: R² = r². For r = 0.9, R² = 0.81.
- What does R² mean?
- It is the proportion of variance in one variable explained by the other, ranging from 0 (none) to 1 (all).
- Can R² be negative?
- For a simple correlation squared, no — it is between 0 and 1. Some regression definitions can dip below 0 for a very poor fit, but r² cannot.
- Does a high R² prove causation?
- No. R² measures how much variation is explained statistically, not whether one variable causes the other.
- Is R² the same as adjusted R²?
- No. Adjusted R² penalises a model for each extra predictor it uses, so it can fall when a useless variable is added. Plain R² never falls when you add predictors, which is why adjusted R² is preferred for comparing multi-variable regressions.