How to Use the Z-Score & Percentile Calculator
This calculator takes a mean (ฮผ), a standard deviation (ฯ), and a data value (x) you want to check, then instantly returns the Z-score and percentile. The Z-score is calculated as (x - mean) รท standard deviation, a standardized measure of how many standard deviations a value sits away from the mean.
A Z-score of 0 means the value equals the mean exactly, a positive score means it's above the mean, and a negative score means it's below the mean. Standardizing values into Z-scores makes it possible to directly compare figures that use different units or distributions โ test scores, height and weight, or quality-control measurements, for example.
The percentile shows what share of the data falls at or below that value, assuming the data follows a normal distribution (computed using an approximation of the standard normal cumulative distribution function). The standard deviation must be greater than 0 โ if it's 0 or negative, the Z-score can't be calculated, and the calculator immediately shows a guidance message.
Frequently Asked Questions
A negative Z-score means the data value is below the mean. For example, Z=-1 means the value is one standard deviation below the mean.
A percentile of 84% means roughly 84% of the data falls at or below that value, assuming the data follows a normal distribution. This is an approximation based on that assumption.