Z-Score Calculator

z = (x − μ) / σ — how many standard deviations a value is above or below the mean.

Inputs

Result

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How to use this calculator

  • Enter the value, mean, and standard deviation.
  • Read the z-score and approximate percentile.

About this calculator

A z-score expresses how many standard deviations a value is from the mean. Positive = above the mean; negative = below. z=1 means one σ above; z=−2 means two σ below. For a normally distributed dataset, z translates directly to a percentile via the normal CDF.

Frequently asked

How big is a "high" z-score?+
|z| > 2 is unusual (~5% chance for normal data). |z| > 3 is rare (~0.3%).
Can z-score be negative?+
Yes — values below the mean produce negative z-scores.
Does z-score require normal data?+
The formula doesn't — it works on any data with a defined mean and SD. The percentile interpretation only holds for approximately normal data.
How does z-score relate to standardization?+
Computing z-scores for every value standardizes the dataset to mean 0, SD 1. Useful for comparing variables on different scales.
Is z-score the same as t-score?+
Similar idea but t-score uses sample SD and a slightly different distribution; t is used for small samples (n < 30).

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