Z-Score Normalize

About this tool

Z-score normalize standardizes a list of numbers so they can be compared on a common scale — a routine first step for statistics, data analysis, and machine learning feature scaling. It offers four common scaling methods:

• Z-score (standardization) — subtracts the mean and divides by the standard deviation, so the output has mean 0 and standard deviation 1. Each result is the standard score (how many standard deviations a value sits above or below the mean). By default it uses the population standard deviation (÷N), matching scikit-learn's StandardScaler and the NumPy default; tick the box to use the sample standard deviation (÷N−1) instead.
• Min-max scaling — linearly rescales values into the 0–1 range, so the smallest value maps to 0 and the largest to 1. Useful when you need a bounded range rather than a zero-centred distribution.
• Max-abs scaling — divides every value by the largest absolute value, so the output stays in −1 to 1 while preserving signs. It is useful for sparse or already-centred data where zeros should remain zeros.
• Robust scaling — subtracts the median and divides by the interquartile range (Q3−Q1). It is less sensitive to outliers than mean/std-dev scaling.

Paste your numbers (separated by spaces, commas, semicolons, or newlines), choose a method, and the tool returns the transformed values in the original order, plus the parameters it used (mean and standard deviation, min/max, max abs, or median/IQR).

How to use it

1. Paste or type your numbers into the Numbers box.
2. Choose the Method — z-score, min-max, max-abs, or robust.
3. For z-score, tick Use sample standard deviation (÷N−1) if your data is a sample rather than the full population.
4. Read off the normalized values, one per line.

Which scaling method should I use?

• Use z-score when you care about how far each value is from the mean in standard-deviation units (e.g. detecting outliers, or feeding features to models that assume roughly zero-centred inputs like SVMs, logistic regression, or PCA).
• Use min-max when you need values in a fixed, bounded range (e.g. 0–1 for a neural-network input layer, or a progress/intensity value).
• Use max-abs when signs matter and zeros should stay zero, especially for sparse numeric features.
• Use robust when outliers would distort the mean and standard deviation; it anchors around the median and IQR instead.

Population vs. sample standard deviation

The population standard deviation divides the summed squared deviations by N; the sample standard deviation divides by N−1 (Bessel's correction), giving an unbiased estimate when your numbers are a sample drawn from a larger population. scikit-learn's StandardScaler and NumPy's std() default to the population form, so that is the default here.

Common uses

• Feature scaling before training a machine-learning model.
• Computing standard scores (z-scores) for exam grades, test results, or benchmarks.
• Outlier detection — values with a large absolute z-score are unusual.
• Rescaling metrics into a common 0–1 or −1 to 1 range for dashboards or comparisons.

Privacy

Everything runs locally in your browser via WebAssembly. Your numbers are never uploaded to a server.

FAQ