Adjusted R² Calculator
Calculate adjusted R-squared, which penalizes R² for added predictor variables.
About Adjusted R² Calculator
Adjusted R² corrects R² for the number of predictors in the model: Adj_R² = 1 − [(1 − R²)(n − 1) / (n − k − 1)], where n is the sample size and k is the number of predictors. Plain R² can only increase (or stay the same) as more predictors are added, even useless ones, which encourages overfitting. Adjusted R² applies a penalty that grows with k, so it can decrease if a new predictor doesn't improve the model enough to justify the added complexity — making it a fairer metric for comparing models with different numbers of features.
Formula
Adj_R^2 = 1 - ((1 - R^2) * (n - 1)) / (n - k - 1)
- R^2
- Coefficient of determination
- n
- Number of samples
- k
- Number of predictors
Worked example
With the default values below, Adjusted R² Calculator returns Adjusted R² of 0.8420. Change any input above and every figure here is recalculated in your browser.
Inputs used
- R²accepts -100–1
- 0.85
- Number of Samples (n)accepts 2–1,000,000,000
- 100
- Number of Predictors (k)accepts 0–1,000,000
- 5
Results
- Adjusted R²
- 0.8420
- Degrees of Freedom (n − k − 1)
- 94
Step by step
- 1Degrees of freedom denominator: n − k − 1= 94
- 2Adjusted R²: 1 − [(1 − R²)(n − 1) / (n − k − 1)]= 0.8420
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why does R² always increase (or stay the same) when adding predictors?
Adding any predictor, even a random and meaningless one, gives the model more flexibility to fit the training data's specific noise, which can only reduce or maintain the residual sum of squares — never increase it — so R² is biased toward preferring more complex models.
Can Adjusted R² be lower than R²?
Yes, and it always will be lower than or equal to R² whenever k > 0; if a predictor doesn't add enough explanatory power to offset the complexity penalty, adjusted R² will decrease even as raw R² stays flat or rises slightly.
How do I choose between multiple models using this metric?
Prefer the model with the highest Adjusted R² among candidates with different numbers of predictors, since it accounts for the tradeoff between explanatory power and model complexity, unlike raw R² which always favors more predictors.