R-Squared Calculator
How Much of the Variance Does the Model Actually Explain?
R² compares a model's predictions against the simplest possible baseline — always predicting the mean — and reports what fraction of the actual variance the model accounts for. An R² of 1 means the predictions match the data perfectly; an R² of 0 means the model does no better than just guessing the average every time; negative values mean the model does worse than that baseline.
The Formula
SS_res is the sum of squared differences between actual and predicted values (residual error); SS_tot is the sum of squared differences between actual values and their mean (total variance). R² expresses residual error as a fraction of total variance and subtracts it from 1.
Where This Matters
- Regression model evaluation — the standard headline metric for how well a linear or nonlinear regression fits observed data.
- Feature selection — comparing R² before and after adding a variable to judge whether it meaningfully improves fit.
- Forecast quality checks — a low or negative R² is a signal that a forecasting model isn't capturing the underlying pattern.
Worked Example
| Quantity | Value |
|---|---|
| SS_res (Σ(actual−predicted)²) | 0.10 |
| SS_tot (Σ(actual−mean)²) | 20.00 |
| R² | 0.995 |
R² = 1 − (0.10 / 20.00) = 0.995, meaning 99.5% of the variance in the actual values is explained by the predictions.
How to Use This Calculator
- Enter the Actual values as a comma-separated list.
- Enter the Predicted values as a comma-separated list of the same length.
- Select Calculate to get R² and the underlying sum-of-squares breakdown.
Related Calculations
See the raw error magnitude behind the same predictions with the Mean Squared Error Calculator, or check classification performance instead with the Confusion Matrix Calculator.