🎯 Z-Score Calculator
Enter a value with its distribution's mean and standard deviation to get the z-score and the percentile it lands at on the standard normal curve.
🎯 Standardise Any Value
What is a Z-Score Calculator?
It expresses a value as its distance from the mean measured in standard deviations, then translates that into a percentile under the normal distribution. By stripping away the original units, a z-score lets you compare observations from completely different scales — a test score against a reaction time, or one sensor's reading against another's.
Use it to gauge how unusual a value is, to standardise features before modelling, or to flag outliers in quality control. Remember the percentile assumes a bell-shaped distribution; for non-normal data the z-score remains meaningful as a standardised distance even if the mapped percentile does not.
❓ Frequently Asked Questions
What is a z-score?
A z-score, or standard score, is the number of standard deviations a value sits from the mean. It is calculated as (value − mean) ÷ standard deviation. A z of 0 is exactly at the mean, +1 is one standard deviation above, and −2 is two below — putting values on any scale onto a common, comparable footing.
How is the percentile derived from the z-score?
The percentile is the area under the standard normal curve to the left of the z-score, expressed as a percentage. This tool computes it with a high-accuracy polynomial approximation of the normal cumulative distribution function (Abramowitz & Stegun 7.1.26). A z of 0 gives the 50th percentile; a z of 1.5 gives about the 93rd.
Does the percentile assume a normal distribution?
Yes. The percentile is exact only when your data follows a normal (bell-shaped) distribution. For skewed or heavy-tailed data the z-score is still a valid standardised distance from the mean, but the percentile it maps to may not match the true rank in your data.
What counts as an unusual z-score?
As a rule of thumb, about 95% of values in a normal distribution fall within ±2 standard deviations and about 99.7% within ±3. So a z-score beyond ±2 is uncommon and beyond ±3 is rare — often flagged as a potential outlier worth investigating.