Standard Score Calculator

About this calculator

The standard score, or z-score, converts a raw value into units of standard deviation from the mean: z = (x − μ) / σ. A z-score of +2 means the value sits two standard deviations above the mean; feeding that z into the standard normal cumulative distribution function gives the value's percentile — the share of the distribution falling below it.

Standardized testing (scaling SAT, GRE, and IQ scores onto a common curve), quality control (Six Sigma processes flag anything beyond roughly ±3σ as out of control), and finance (risk metrics that measure how extreme a return is relative to its historical distribution) all lean on z-scores. Researchers and teachers use them to compare values measured on different scales, and to spot outliers in a dataset.