Z-Score Calculator
A z-score expresses a value in standard deviation units: z = (x − μ) / σ. Enter your raw value with the mean and standard deviation — or type a z directly — and get the percentile rank plus all three tail probabilities: P(Z < z), P(Z > z) and the two-tailed probability used in significance testing. The normal probabilities match R's pnorm to at least six significant digits, so the results agree with standard z-tables and any statistics package. Typical uses: comparing scores from different scales (IQ, test norms, lab values), spotting outliers, and converting a z into the p-value of a z-test.
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Frequently asked questions
How do I report a z-score in APA 7 format?
For a z-test, report the statistic and exact p-value: "z = 1.96, p = .050". As a descriptive standard score, give the value with its reference mean and SD, e.g. "the score was 2.0 SD above the mean (z = 2.00, 98th percentile)". The AI Report writes the full APA sentence from your numbers.
What does a z-score actually tell me?
How many standard deviations a value sits above (positive z) or below (negative z) the mean. Because z removes the original units, scores from different scales become comparable. Under a normal distribution roughly 68% of values fall within ±1, 95% within ±2, and 99.7% within ±3.
How is the z-score related to the percentile?
The percentile is the normal cumulative probability P(Z < z) times 100. A z of 0 is the 50th percentile, z = 1.28 is about the 90th, z = 1.64 about the 95th. This mapping is exact only if the underlying distribution is (approximately) normal.