If you need a fast, practical way to compute R² (the coefficient of determination), this tool gives you three options: from a correlation coefficient, from sums of squares, or from raw actual/predicted data. It is useful for regression analysis, forecasting checks, and model performance reporting.
R² Calculator
Choose your input method, enter values, and click Calculate.
Valid range: -1 to 1. Formula: R² = r²
Formula: R² = 1 - (SSE / SST)
Use commas, spaces, or new lines. Both lists must have the same length.
What is the coefficient of determination?
The coefficient of determination, usually written as R², measures how much of the variation in your dependent variable is explained by your model. In simple terms, it tells you how well your regression line (or model predictions) fits your observed data.
An R² of 0.80 means your model explains about 80% of the variance in the outcome. The remaining 20% is unexplained by the model (noise, missing predictors, randomness, or model misspecification).
Formulas used by this calculator
1) From correlation coefficient
For simple linear regression with one predictor, R² can be computed directly from the Pearson correlation coefficient:
R² = r²
2) From sums of squares
If you have model fit statistics from software output:
- SSE: Sum of Squared Errors (unexplained variation)
- SST: Total Sum of Squares (total variation)
Then:
R² = 1 − (SSE / SST)
3) From raw actual vs. predicted values
When you enter observed and predicted data, this page computes:
- SSE = Σ(y − ŷ)²
- SST = Σ(y − ȳ)²
- R² = 1 − SSE/SST
How to use this R squared calculator
Method A: Correlation route
If you only know the correlation coefficient between X and Y, select From correlation (r), enter r, and calculate. This is the fastest method for simple regression summaries.
Method B: Model diagnostics route
If you already have SSE and SST from Excel, R, Python, SPSS, or another stats tool, select From SSE and SST. Enter both values and calculate R² immediately.
Method C: Raw predictions route
If you have two lists (actual values and model predictions), select From actual and predicted values. Paste each list and calculate. This is ideal for quick model evaluation without manually computing errors.
Interpreting your result
R² values are context-dependent. A “good” R² in social science may be lower than what is expected in physics or controlled engineering systems.
- R² near 1: strong explanatory power
- R² around 0.5: moderate explanatory power
- R² near 0: little explanatory power
- Negative R²: model performs worse than predicting the mean (possible in some settings)
Important caveats
High R² does not prove causation
R² measures fit, not cause-and-effect relationships. Always pair regression fit with domain knowledge and proper study design.
R² alone is not enough
A complete model review should include residual plots, RMSE/MAE, outlier checks, and possibly adjusted R² for multiple predictors. For prediction tasks, evaluate performance on held-out data.
Watch for overfitting
Adding more predictors often increases R² on training data, even when those predictors are not useful. Consider adjusted R² and cross-validation to judge generalization quality.
Quick example
Suppose SST = 250 and SSE = 40. Then:
R² = 1 − 40/250 = 1 − 0.16 = 0.84
This means the model explains about 84% of the variation in the observed outcome.
Frequently asked questions
Can R² be negative?
Yes. Although many introductory examples show values between 0 and 1, R² can be negative when predictions are worse than simply using the mean of the observed data.
Is a higher R² always better?
Not always. A higher R² can still come from an overfit model that fails on new data. Use additional metrics and validation strategies.
Is R² the same as adjusted R²?
No. Adjusted R² penalizes unnecessary predictors and is often more informative for multiple regression model comparison.