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.

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