Z-score calculator (standard score)
Calculate the z-score of a value and its percentile in the normal distribution.
The z-score tells how many standard deviations the value is from the mean. Positive is above the mean; negative, below. The percentile assumes a normal distribution.
How the calculation works
The z-score standardizes a value: z = (x − mean) ÷ standard deviation. A z of 1.5 means 1.5 std. devs above the mean. In a normal distribution, that maps to a percentile (the fraction of values below it).
Examples
- Score 80, mean 70, SD 5: z = 2 → two SDs above the mean.
- z = 0 means exactly at the mean; a negative z is below it.
Frequently asked questions
What is a z-score for?
To compare values on different scales and see how "rare" a value is — common in exams, quality control and statistics.
What is the 68-95-99.7 rule?
In a normal distribution, ~68% of values are within 1 SD, ~95% within 2 and ~99.7% within 3.
Can z-scores compare different tests?
Yes — that is a main use. A 7 on a hard test can have a higher z than an 8 on an easy one.
What does a z-score of 2 mean?
The value sits two standard deviations above the mean. In a normal distribution about 97.7% of data falls below it.
What z-score counts as an outlier?
There is no universal cutoff. |z| > 2 flags attention and |z| > 3 strongly suggests an outlier, since only 0.3% of data lies beyond three deviations.
Does standardising make data normal?
No. It only shifts the mean to 0 and scale to 1; the shape is unchanged.
When should I use t instead of z?
When the population standard deviation is unknown and the sample is small (under about 30). The t distribution has wider tails.
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See all →Updated on June 30, 2026 · by Rafael Rossi · Methodology & sources