How do you normalize data between 0 and 1?

Use Min-Max normalization: for each value, subtract the column minimum and divide by the range (max − min). The smallest value becomes 0, the largest becomes 1, and everything else lands proportionally in between. For example, in [10, 20, 30, 40, 50] the value 20 maps to (20 − 10) / (50 − 10) = 0.25.

What is the difference between normalization and standardization?

Normalization (Min-Max) rescales values into a fixed range such as 0 to 1, so it is bounded but sensitive to outliers. Standardization (Z-score) centres the data on a mean of 0 and a standard deviation of 1, so it is unbounded but keeps the shape of the distribution. Use Min-Max for bounded inputs like image pixels; use Z-score when an algorithm assumes roughly centred, unit-variance features.

What formula does StandardScaler use in scikit-learn?

StandardScaler computes z = (x − mean) / std, where std is the population standard deviation — it divides the sum of squared deviations by N, not N − 1 (ddof = 0). This tool defaults to the same population basis so its numbers match scikit-learn's fit_transform output. A toggle lets you switch to the sample standard deviation (÷ N − 1) if your workflow needs it.

When should I use robust scaling instead of standardization?

Use Robust scaling when your data has outliers. It centres on the median and scales by the interquartile range (Q3 − Q1) instead of the mean and standard deviation, so a few extreme values barely move the result. Z-score standardization, by contrast, lets one large outlier inflate the standard deviation and squash every other value toward zero.

Does MinMaxScaler use population or sample standard deviation?

Neither — MinMaxScaler does not use the standard deviation at all. It only uses the column minimum and maximum: x_scaled = (x − min) / (max − min), then optionally rescaled to a target range. The population-versus-sample question applies to StandardScaler (Z-score), which uses the population standard deviation by default in scikit-learn.

What happens when every value is the same?

The denominators collapse to zero, so scikit-learn substitutes a safe no-op rather than dividing by zero. Min-Max maps every element to the target minimum, Z-score and Robust return 0 for every element, and MaxAbs returns the values divided by their absolute value (so a constant like [7, 7, 7] becomes [1, 1, 1], or [0, 0, 0] if the constant itself is zero). This tool follows the same rules and flags the affected column.

How are the quartiles for robust scaling calculated?

Q1, the median, and Q3 use linear interpolation, the NumPy and RobustScaler default. For a sorted array of length n, the p-th quantile sits at position h = (n − 1) · p; the value is interpolated between the two neighbouring sorted points. This is why [2, 4, 4, 4, 5, 5, 7, 9] gives Q1 = 4, median = 4.5, and Q3 = 5.5.

Is my data uploaded anywhere?

No. Every calculation runs in your browser with JavaScript — the numbers you paste never leave your device and nothing is stored or logged. You can disconnect from the internet after the page loads and the calculator still works.

Data Science · Machine Learning

Feature Scaling & Normalization Calculator

Paste a column of numbers and instantly rescale it four ways — Min-Max normalization, Z-score standardization, MaxAbs, and Robust scaling — using the exact scikit-learn formulas, with every fitted parameter shown so you can check the arithmetic by hand.

By Induwara Ashinsana— Executive Director, Ryzera TechnologiesUpdated Jul 13, 2026

Scale & normalize your data

scikit-learn formulas

Your data column (numbers)

Separate values with commas, spaces, or new lines. 2–1000 numbers.

Try

Min-Max target min

Min-Max target max

Std dev basis

Population ÷N (sklearn)Sample ÷(N−1)

Decimal places

Fitted parameters

count (n)

min

10.0000

max

50.0000

range

40.0000

mean (μ)

30.0000

std (σ, ÷N)

14.1421

median

30.0000

20.0000

40.0000

IQR

20.0000

max |x|

50.0000

Scaled values

#	Original	Min-Max	Z-score	MaxAbs	Robust
1	10	0.0000	-1.4142	0.2000	-1.0000
2	20	0.2500	-0.7071	0.4000	-0.5000
3	30	0.5000	0.0000	0.6000	0.0000
4	40	0.7500	0.7071	0.8000	0.5000
5	50	1.0000	1.4142	1.0000	1.0000

Formulas and edge-case behaviour follow scikit-learn's preprocessing documentation. StandardScaler uses the population standard deviation (÷N) by default. All maths runs in your browser — nothing is uploaded.

How it works

Feature scaling puts columns that live on different numeric ranges onto a common footing so that distance- and gradient-based models — k-nearest neighbours, SVMs, k-means, PCA, and neural nets — are not dominated by whichever feature happens to have the largest units. This calculator fits and applies the four transforms defined in the scikit-learn preprocessing guide to a single feature vector X = [x₁, …, xₙ].

Min-Max normalization (MinMaxScaler): x_std = (xᵢ − min) / (max − min), then map to a target range [a, b] with x_scaled = x_std · (b − a) + a. The default range [0, 1] reduces to x_std. A constant feature (max = min) maps to the range minimum a.
Z-score standardization (StandardScaler): x_scaled = (xᵢ − μ) / σ, with mean μ = (1/n)·Σxᵢ. scikit-learn uses the population standard deviation σ = √((1/n)·Σ(xᵢ − μ)²) (ddof = 0). A sample-basis toggle switches the divisor to n − 1. Zero variance yields 0 for every element.
MaxAbs scaling (MaxAbsScaler): x_scaled = xᵢ / max(|X|). It maps data into [−1, 1] without shifting the centre, which preserves sparsity (zeros stay zero). If the largest magnitude is 0, the output is 0.
Robust scaling (RobustScaler): x_scaled = (xᵢ − median) / IQR, where IQR = Q3 − Q1. Quartiles use linear interpolation (the NumPy default): for a sorted array the p-th quantile sits at position h = (n − 1)·p and is interpolated between neighbouring points. Because it uses the median and IQR, outliers barely affect it.

The fitted parameters panel shows every number the scalers depend on — min, max, range, mean, standard deviation, median, Q1, Q3, IQR, and maximum absolute value — so each output can be reproduced by hand. As a correctness check, the population standard deviation is computed two algebraically independent ways: the sum of squared deviations, and the moment identity Var = E[X²] − (E[X])². When they agree, the panel shows a “σ verified” badge.

Worked examples

Basic ramp — [10, 20, 30, 40, 50]

Parameters: min=10, max=50, range=40, μ=30, σ=√(200)=14.1421, median=30, IQR=20, max|x|=50
Min-Max: (20 − 10) / 40 = 0.25 → [0, 0.25, 0.5, 0.75, 1]
Z-score: (20 − 30) / 14.1421 = −0.7071 → [−1.4142, −0.7071, 0, 0.7071, 1.4142]
MaxAbs: 20 / 50 = 0.4 → [0.2, 0.4, 0.6, 0.8, 1]
Robust: (10 − 30) / 20 = −1.0 → [−1, −0.5, 0, 0.5, 1]

Textbook σ = 2 with quartiles — [2, 4, 4, 4, 5, 5, 7, 9]

Mean μ = 40 / 8 = 5; deviations (−3,−1,−1,−1,0,0,2,4); Σ(dev²) = 32
Population σ = √(32 / 8) = √4 = 2
Z-score: (2 − 5)/2 = −1.5 → [−1.5, −0.5, −0.5, −0.5, 0, 0, 1, 2]
Quartiles (linear): Q1 pos = 7·0.25 = 1.75 → 4; median pos = 3.5 → 4.5; Q3 pos = 5.25 → 5.5; IQR = 1.5
Robust: (2 − 4.5)/1.5 = −1.6667 → [−1.6667, −0.3333, −0.3333, −0.3333, 0.3333, 0.3333, 1.6667, 3]

Edge case — constant data [7, 7, 7]

range = 0, σ = 0, IQR = 0 → every scaler that divides would hit 0/0
Min-Max: maps to the target minimum → [0, 0, 0] (for range [0, 1])
Z-score: with_std no-op → [0, 0, 0]
Robust: zero IQR no-op → [0, 0, 0]
MaxAbs: 7 / |7| = 1 → [1, 1, 1] (only 0 if the constant is itself 0)

Frequently asked questions

Sources & references

Formulas and edge-case behaviour were last cross-checked against the scikit-learn documentation on 2026-07-13. Both worked examples were reconciled by hand and against scikit-learn's fit_transform output.

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Comments & feedback

Spotted a bug or want an improvement? Tell us — our team reviews every comment, and good ideas get built. Comments are public and anonymous.

Found a bug, edge case, or want another scaler added?

Email me at [email protected] — most fixes ship within 24 hours.