Percentile from Z-Score Calculator

About this calculator

A z-score measures how many standard deviations a value sits from the mean of a normal distribution. This calculator converts that z-score into a percentile using the standard normal cumulative distribution function, Φ(z) — the area under the bell curve to the left of z — so a z-score of 0 returns the 50th percentile, +1.0 returns roughly the 84th percentile, and −1.96 returns roughly the 2.5th percentile.

Because so many natural and measured quantities are approximately normally distributed, this z-to-percentile conversion underlies standardized test score reports, growth charts, and IQ scores, as well as statistical hypothesis testing where a z-score beyond ±1.96 corresponds to the common 5% two-tailed significance threshold. Statisticians, teachers scoring standardized assessments, and researchers running hypothesis tests use this conversion constantly to translate a raw z-score into a percentage that's easy to interpret and communicate.