Z-Score Calculator
Calculate z-scores, percentiles, and p-values from a value or directly from a z-score.
About Z-Scores
A z-score (standard score) measures how many standard deviations a data point is from the mean of its distribution. A z-score of 0 means the value equals the mean; positive z-scores are above the mean, and negative z-scores are below. Z-scores allow you to compare values from different distributions.
The Standard Normal Distribution
The percentile (cumulative distribution function) is calculated using the normal distribution. About 68% of values fall within z = ±1, 95% within z = ±1.96, and 99.7% within z = ±3 (the empirical rule).
P-Values from Z-Scores
The one-tailed p-value is the probability of observing a value as extreme as z in one direction. The two-tailed p-value accounts for both directions and is 2 × min(Φ(z), 1 − Φ(z)). A p-value below 0.05 is typically considered statistically significant.
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For a related calculation, use Confidence Interval Calculator to calculate confidence intervals for a population mean using Z or t critical values at 90%, 95%, or 99%. Alternatively, use Permutation and Combination Calculator to calculate P(n,r) permutations and C(n,r) combinations with factorial working and Pascal's triangle.
For the underlying method, read Understanding Standard Deviation and Why It Matters.