Z-score calculator
z = (x − mean) / standard deviation. A z-score of 0 is exactly average; positive is above the mean, negative below, measured in standard deviations rather than the original units — which is what makes it usable to compare values from different distributions.
What a z-score is
A z-score says how many standard deviations a value sits from the mean: z = (x - mean) / standard deviation. A z-score of 0 is exactly average. Positive is above the mean, negative is below it, and the size of the number is the distance in standard deviations, not in the original units - which is what makes z-scores usable to compare two values measured on different scales.
Both directions
Enter a value with a mean and standard deviation to get its z-score, or enter a z-score with a mean and standard deviation to get the value it corresponds to - useful when a report gives you the z-score and you need the actual figure back.
Reading the percentile
Alongside the z-score, this shows the percentile - the percentage of a normal distribution that falls below that value - computed from the standard normal cumulative distribution function. A z-score of 1.0 sits at roughly the 84th percentile; -1.0 sits at roughly the 16th. This is what turns "1.5 standard deviations above average" into "about the 93rd percentile", the form most people actually reason in.
Where this is used
Test scores, growth charts, quality control charts and outlier detection all lean on z-scores because they make values from different distributions directly comparable. A standard deviation of 0 is refused, since dividing by it is undefined - every value would technically be infinitely far from the mean.
Related tools
See also the quartile calculator for a different way of describing a spread of data.
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