Feature Scaling Calculator
Putting Every Feature on the Same Footing
A feature measured in dollars and a feature measured in years can't be compared fairly by algorithms that rely on distance or magnitude — the dollar feature will dominate simply because its numbers are bigger, not because it's more important. Scaling transforms every feature onto a common range or distribution before that comparison happens.
The Formula
Standardization (Z-Score): z = (x − μ) / σ
Min-max normalization compresses every value into the 0–1 range. Standardization instead centers the data at a mean of 0 with a standard deviation of 1, which is less sensitive to a single extreme outlier but doesn't bound the result to a fixed range.
Where This Matters
- Distance-based algorithms — K-nearest neighbors, K-means clustering, and SVMs all need comparable feature scales to work correctly.
- Gradient descent convergence — neural networks and linear models trained with gradient descent typically converge faster on scaled features.
- Regularization — L1/L2 regularization penalties are only fair across features when those features are on the same scale.
Worked Example
| Original | Min-Max (0–1) | Z-Score |
|---|---|---|
| 10 | 0.00 | −1.4142 |
| 20 | 0.25 | −0.7071 |
| 30 | 0.50 | 0.0000 |
| 40 | 0.75 | 0.7071 |
| 50 | 1.00 | 1.4142 |
Mean = 30, population standard deviation ≈ 14.1421. Min-Max uses min=10, max=50.
How to Use This Calculator
- Choose Min-Max Normalization or Standardization (Z-Score) as the scaling method.
- Enter the Values as a comma-separated list.
- Select Calculate to get every value transformed onto the new scale.
Related Calculations
Once features are scaled, distance-based comparisons become more meaningful — try the Euclidean Distance Calculator or the Cosine Similarity Calculator.