Min-Max Normalization Calculator: rescale data to 0–1 or any range

How it works

x′ = lo + (x − min) ÷ (max − min) × (hi − lo) · for 0–1: x′ = (x − min) ÷ (max − min) · reverse: x = min + (x′ − lo) ÷ (hi − lo) × (max − min)

Min-max normalization stretches or squeezes a list linearly so its smallest value lands on a chosen lower bound and its largest on an upper bound, most often 0 and 1. Every value keeps its place and relative spacing, because the whole transformation is one straight line x′ = a·x + b (shown in the results). It is the usual way to put features on a common scale for k-nearest neighbours, neural networks and dashboards, and it is what scikit-learn’s MinMaxScaler does. By default the min and max come from the list itself. Choose fixed bounds when new data must be scaled exactly like earlier (training) data, or when the scale has known limits such as 0–10 ratings or 0–255 pixel values; values outside the bounds then fall outside the target range unless you turn on clipping. You can also normalize one value or turn a normalized value back into the original units. The weakness of min-max scaling is outliers: one extreme value sets the range and compresses everything else toward one end, so the calculator flags values beyond 1.5 × IQR.

Worked example

For 20, 40, 60, 80, 100 with target 0–1: min = 20 and max = 100 give a range of 80. The value 40 becomes 0 + (40 − 20) ÷ 80 × 1 = 0.25, and 60 becomes 0.5, so the list is 0, 0.25, 0.5, 0.75, 1 with a mean of 0.5. The scaling line is x′ = 0.0125 × x − 0.25. With target 0–100 the same list becomes 0, 25, 50, 75, 100.

Sources: Feature scaling — Wikipedia · MinMaxScaler — scikit-learn documentation

Frequently asked questions