Z-Score to Percentile Calculator

About this calculator

This calculator converts a z-score — how many standard deviations a value sits from the mean — into a percentile using the cumulative distribution function (CDF) of the standard normal distribution, Φ(z). The percentile equals Φ(z)×100, found by integrating the standard normal probability density function from −∞ to z; a z-score of 0 gives the 50th percentile, +1.96 gives about the 97.5th, and −1.96 gives about the 2.5th.

Statisticians, researchers, teachers grading on a curve, and students use this to interpret standardized test scores (SAT, IQ tests), lab results in clinical medicine, and hypothesis-testing output where a z-statistic needs to be translated into a probability or percentile rank. Enter a z-score to get its percentile, or use it alongside a raw score, mean, and standard deviation.