NumberTally Z-Score Calculator
Compute the z-score — z = (x − mean) / standard deviation — and see which percentile it corresponds to, using a proper normal-distribution calculation (not a lookup guess). Enter any value, mean, and SD; results update instantly. Free, no sign-up.
Advanced options
Leave blank to skip. Finds the value x that sits at the given percentile of this distribution.
What the z-score tells you
A z-score counts standard deviations from the mean: z = 1 means one SD above average, z = −2 means two SD below. Because many real-world measurements (test scores, heights) are roughly bell-shaped, the z-score converts directly to a percentile — z = 1 lands at about the 84th percentile, z = 2 at about the 97.7th.
The 68–95–99.7 rule
For a normal distribution, about 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD. The bell curve below shades the area up to your value so you can see exactly where it sits.
Frequently Asked Questions
What does a z-score of 1.5 mean?
The value is 1.5 standard deviations above the mean — roughly the 93rd percentile, so it beats about 93% of the distribution.
Can z-scores be negative?
Yes — a negative z-score simply means the value is below the mean. z = −1 sits at about the 16th percentile.
What is the difference between a z-score and a percentile?
The z-score is measured in standard-deviation units; the percentile is the share of values below it. This calculator converts one to the other using the normal distribution.
Should I use the population or the sample standard deviation?
Use whichever SD describes the reference distribution. For standardized tests the published SD is effectively the population value; for your own data, the sample SD from our statistics calculator works.
How accurate is the percentile?
The math (Abramowitz–Stegun error-function approximation) is accurate to about 7 decimal places. The real-world caveat is whether your data is actually bell-shaped — percentiles assume normality.