Z-Score and Percentile Calculator

This z-score and percentile calculator tells you how far a value sits from the mean, measured in standard deviations, and what percentile that position represents under a normal distribution. You enter the value you want to assess, the mean of the data and the standard deviation, and the tool returns the z-score and the matching percentile. The z-score is the value minus the mean, divided by the standard deviation, so a z-score of zero sits exactly at the mean, a positive z-score is above the mean and a negative one is below. The percentile uses the normal cumulative distribution to tell you the share of the population that falls below your value, using a precise error function approximation. Students, teachers, researchers and anyone comparing scores across different tests use z-scores to put numbers on a common scale, since a raw mark means little without knowing the spread of the rest of the group. Three tips help you read the result well. First, a z-score of about 1.96 corresponds to roughly the 97.5th percentile, which is why it appears in 95 percent confidence intervals. Second, the percentile only makes sense if the data is roughly bell shaped, so for very skewed data a percentile from the normal curve can mislead. Third, always use the standard deviation of the same group the value belongs to, because mixing a value from one group with the spread of another gives a meaningless z-score. Reporting both the z-score and the percentile makes a result easy to compare across tests and groups.

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1.50
Z-score
Percentile93.3%
Below this value93.3% below

z = (x - mean) / sd. Percentile from the normal CDF. Estimate only, not financial or tax advice.

How it works

The z-score is the value minus the mean, divided by the standard deviation. The percentile is the area under the standard normal curve to the left of that z-score, found with an error function approximation. A z-score of zero gives the 50th percentile.

Worked example

With a value of 85, a mean of 70 and a standard deviation of 10, the z-score is 85 minus 70, divided by 10, which is 1.50. Reading the normal curve, a z-score of 1.50 sits at about the 93.3rd percentile, so roughly 93.3 percent of values fall below it.

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Frequently asked questions

What does a z-score tell me?

A z-score tells you how many standard deviations a value is above or below the mean. A z-score of 2 means the value is two standard deviations above the mean, while minus 1 means one standard deviation below. It puts values from different scales onto one common measure.

How is a z-score turned into a percentile?

The percentile is the area under the normal curve to the left of the z-score, found with the normal cumulative distribution. A z-score of zero gives the 50th percentile, and higher z-scores give higher percentiles. This calculator uses an accurate error function approximation to compute it.

Does the percentile work for any data?

It assumes the data follows a roughly normal, bell shaped distribution. For data that is heavily skewed or has long tails, a percentile read from the normal curve can be misleading. In those cases an empirical percentile from the actual data is more reliable.