What a z-score measures
A z-score restates a raw value as a distance from the mean, counted in standard deviations. Subtract the mean from your value and divide by the standard deviation: the result tells you not just whether the value is above or below average, but by how much relative to the typical spread. A z of +2 means the value sits two standard deviations above the mean; a z of −1 means one standard deviation below.
Because the units cancel out, z-scores let you compare measurements from different scales — a test score and a height, for example — on the same footing.
From z-score to percentile
When the underlying data is roughly normal (bell-shaped), each z-score maps to a percentile: the proportion of the distribution that falls below the value. This calculator uses the standard normal cumulative distribution to make that conversion.
- z = 0 is exactly the mean, the 50th percentile.
- z = +1 sits near the 84th percentile; z = −1 near the 16th.
- About 95% of a normal distribution lies between z = −2 and z = +2.
Interpreting results with care
A large absolute z-score flags a value as unusual for its distribution, which is why z-scores are used to spot outliers and to standardise data before further analysis.
The percentile here assumes a normal distribution. If your data is strongly skewed or has heavy tails, the z-score itself is still valid as a standardised distance, but the percentile estimate can be off. Check the shape of your data before reading the percentile literally.
Formula
z = (x − mean) / stdDevFrequently asked questions
- What does the percentile mean?
- Assuming the data is normally distributed, the percentile is the share of values that fall below this one. A z-score of 0 corresponds to the 50th percentile.