Free Z-Score Calculator

Standardise values, find percentiles, and compute probabilities for normal distribution problems in homework and exams.

Determine whether a patient measurement (blood pressure, BMI, lab result) is unusual relative to population norms.

Convert raw test scores to z-scores to compare performance across tests with different scales and difficulties.

Determine how many standard deviations a process measurement is from the specification limit to assess process capability.

Measure how unusual a price movement or return is relative to historical mean and volatility (standard deviation).

Z-scores enable you to compare values from completely different distributions. A student who scores 85 on Test A (mean=70, SD=10) has z=1.5. A student scoring 72 on Test B (mean=60, SD=6) has z=2.0. Despite the lower raw score, the Test B student performed better relative to their peers — a fact invisible without z-scores.

The empirical rule provides powerful quick estimates: z > 1.96 → top 2.5%; z > 2.58 → top 0.5%; z > 3.29 → top 0.05%. These thresholds correspond to α = 0.05, 0.01, and 0.001 in statistical hypothesis testing — the most commonly used significance levels in academic research.

In finance, z-scores measure investment volatility. The Altman Z-score (a different formula) predicts corporate bankruptcy. In quality control, the process capability index Cpk is related to how many sigma (standard deviations) a process operates from its specification limits — a 6-sigma process has an incredibly low defect rate of 3.4 per million.

When converting between z-score and percentile, remember that the normal distribution is symmetric. A z-score of +1.0 is the 84.1st percentile; z = −1.0 is the 15.9th percentile (100 − 84.1). You only need to know the upper-tail probabilities to get lower-tail values by symmetry.