Z-Score Calculator

A z-score, also called a standard score, tells you how many standard deviations a value sits above or below the mean. A positive z-score is above the mean, a negative one is below, and 0 lands exactly on the mean. This z score calculator takes the value, the mean, and the standard deviation as three direct inputs and returns the z-score for you.

How to use this calculator

1. Enter the value (x) you want to measure — the single data point you care about.
2. Enter the mean of the data set the value comes from.
3. Enter the standard deviation of that same data set.

The calculator subtracts the mean from your value, divides by the standard deviation, and shows the z-score. A result near 0 means the value is typical; a large positive or negative result means it is unusually high or low.

Worked example

Suppose a value of 72 comes from a data set with a mean of 68 and a standard deviation of 5. Apply the z score formula:

z = (x − mean) / standard deviation
z = (72 − 68) / 5
z = 4 / 5
z = 0.8

So 72 sits 0.8 standard deviations above the mean of 68 — a little above average, but well within the normal range. For the conventions behind standard scores and the standard normal curve, see the NIST/SEMATECH e-Handbook on the standard normal distribution.

Frequently asked questions

What does a negative z-score mean?

A negative z-score means the value falls below the mean. For example, a z-score of −1.5 sits one and a half standard deviations below the average.

What is a typical z-score range?

For most data sets, nearly all values fall within ±3 standard deviations of the mean, so z-scores usually land between −3 and 3. A z-score outside that range points to an unusual or outlying value.

Is a z-score the same as a percentile?

No. A z-score measures distance from the mean in standard deviations, while a percentile tells you what share of values fall below a point. You can convert a z-score to a percentile using a standard normal table.