Read a z-score back into plain language
How many standard deviations from the mean is a value — and what share of the distribution sits above or below it? Percentile, one- and two-tailed areas.
Tools used in this guide
The job
A test score of 82 means little until it is placed inside its distribution. The z-score standardizes it against the mean and standard deviation; the percentile then says what fraction of the population falls below it.
Standardize the value
Enter the raw value, the mean, and the standard deviation. Results show the z-score, the percentile rank, the upper-tail probability, and a plain-language direction line — the numbers used to read significance at a glance.
- z = 1.96 is the classic two-tailed 5% boundary — for a two-tailed check, double the upper-tail probability shown.
- A negative z is a below-average value; the percentile mirrors accordingly.
Worked example
Score 82 on a mean-70, SD-10 test: z = 1.2, percentile ≈ 88.5. About 11.5% of the distribution sits higher.
Where it stops
It assumes a normal distribution — for skewed data the percentile is a model, not a fact. It does not run hypothesis tests or compute sample statistics. Inputs are capped at 1e12 and the standard deviation must be positive.