Percentile to Z-Score Calculator

About this calculator

In a standard normal distribution, the z-score is the inverse of the cumulative distribution function: given a percentile p (as a proportion between 0 and 1), the calculator finds the value z such that Φ(z) = p, meaning the area under the standard normal curve to the left of z equals p. There's no closed-form formula for Φ⁻¹, so it's evaluated numerically.

Statisticians and psychometricians use this to convert a percentile rank on a standardized test — IQ scores, SAT/GRE percentiles, growth charts — into the z-score used in further statistical calculations, and quality-control engineers use it in Six Sigma work to relate a defect percentile to a standard-deviation threshold.