The formula
How it works
A z-score says how many standard deviations a value sits above or below the mean. It turns a raw number into a position on the bell curve, so scores from completely different scales can be compared directly.
FAQ
What does a negative z-score mean?
It means the value is below the mean. A z-score of 0 is exactly average, positive scores are above average, and negative scores are below. The size tells you how far, in standard deviations.
What is the percentile shown?
It is the share of a normal distribution that falls below your value. A z-score of 2, for instance, sits at about the 98th percentile — higher than 98% of the data.
Does this calculator assume a normal distribution?
Yes — the percentile is computed from the standard normal curve, so it is most accurate when the underlying data is roughly bell-shaped. The z-score itself can be calculated for any data, but the percentile interpretation is only reliable for normal or near-normal distributions.
What counts as an unusual z-score?
As a rule of thumb, z-scores beyond ±2 are often considered notable, and beyond ±3 quite rare, since a normal distribution has about 95% of values within 2 standard deviations of the mean and over 99.7% within 3.
What is the difference between a z-score and a t-score?
A z-score assumes you know the true population standard deviation and works well with large samples, while a t-score is used when the standard deviation is estimated from a small sample and follows a slightly wider t-distribution to account for that extra uncertainty.
Can I use a z-score to compare two different data sets?
Yes — that is one of its main purposes. Because z-scores strip away the original units and rescale everything to standard deviations from the mean, a z-score of 1.5 means the same relative position whether it comes from test scores, heights or sales figures.
How is the z-score related to a confidence interval?
Standard z-values — like 1.96 for 95% confidence — mark how many standard deviations from the mean a given percentage of a normal distribution falls within, and those same values are used to build confidence intervals around an estimate.
About the z-score calculator
This calculator finds the z-score of a value — also called a standard score — and the percentile that goes with it. A z-score rescales a number by measuring it in standard deviations from the mean, which strips away the original units. That is what makes it so useful: a test mark, a height and a blood-pressure reading can all be turned into z-scores and compared on the same footing.
How to use it
Enter the value you are interested in, the mean of the data set, and its standard deviation. The calculator returns the z-score and the matching percentile from the normal distribution. For example, an IQ of 130 with a mean of 100 and a standard deviation of 15 gives a z-score of 2 — two standard deviations above average, at roughly the 98th percentile. A value equal to the mean gives a z-score of 0.
The formula
The z-score is , where is the value, is the mean and is the standard deviation. You subtract the mean to see how far the value is from the centre, then divide by the standard deviation to express that gap in standard-deviation units. To turn a z-score into a percentile, you look up the area to its left under the standard normal curve, which the calculator computes for you.
Where it is used
Z-scores are a staple of statistics and testing. Standardised exams report them so results are comparable year to year, and doctors use them — as “standard deviation scores” — to track a child’s growth or bone density against healthy norms. In finance they flag unusual price moves, in manufacturing they drive quality control, and in any hypothesis test the z-score is the bridge between a raw measurement and a probability.