Coefficient of Determination Calculator (R²)

R² is a statistical measure that indicates what proportion of the variance in the dependent variable (Y) can be explained by the independent variable (X) in a regression model. It ranges from 0 to 1, where 1 means the model perfectly explains all variance and 0 means it explains none.

Simply enter your X values in the first box and your corresponding Y values in the second box. Values can be separated by commas, spaces, or new lines. Make sure each X value has a matching Y value, then click Calculate to get R², the correlation coefficient, adjusted R², and the regression equation.

R² = 1 − (SS_res / SS_tot), where SS_res is the sum of squared residuals (Σ(yᵢ − ŷᵢ)²) and SS_tot is the total sum of squares (Σ(yᵢ − ȳ)²). Alternatively, R² is simply the square of the Pearson correlation coefficient r, so R² = r².

An R² of 0.9 means 90% of the variance in Y is explained by X — a very strong fit. Values above 0.7 are generally considered strong, 0.4–0.7 moderate, and below 0.4 weak. Context matters though: in social sciences an R² of 0.3 can be meaningful, while in physics 0.99 might be expected.

Adjusted R² penalizes for adding unnecessary predictor variables to a model. For simple linear regression (one X variable), adjusted R² = 1 − (1 − R²) × (n − 1) / (n − 2). It is always less than or equal to R² and is more informative when comparing models with different numbers of predictors.

R² is the square of the Pearson correlation coefficient r. While r measures both the strength and direction of a linear relationship (ranging from −1 to 1), R² only measures strength (ranging from 0 to 1). For example, if r = −0.9, then R² = 0.81, telling you 81% of variance is explained regardless of direction.

You need at least 3 paired data points to calculate a meaningful R². With only 2 points, R² will always equal 1 since any two points perfectly define a line. More data points generally produce more reliable and statistically significant results.

Not necessarily. A high R² indicates the model explains much of the variance, but it doesn't confirm the relationship is linear, that the model is correctly specified, or that causation exists. Always visualize your data with a scatter plot and check residuals to validate your regression assumptions.