Z-Score Calculator (Standard Score & Percentile)
Compute z-score, percentile rank, and one/two-tailed p-values under the standard normal distribution. z = (x − μ) / σ.
MATHCompute the standard score (z-score) of a value, its percentile rank, and one/two-tailed tail probabilities under the standard normal distribution. Formula: z = (x − μ) / σ.
Common benchmarks: z = ±1.96 is the 95% confidence boundary (two-tailed p = 0.05); z = ±2.58 is 99% (p = 0.01); z = ±3 means only 0.27% of values are this extreme. About 68% of values fall within ±1σ, 95% within ±2σ, 99.7% within ±3σ (empirical rule).
Z-Score Calculator
Compute the standard score (z-score) of a value, the percentile rank, and tail probabilities under the standard normal distribution. Formula: z = (x − μ) / σ.
Common Z-Score Benchmarks
- z = 0 — exactly the mean, 50th percentile.
- z = ±1 — 1 standard deviation, ~68% of values fall within ±1σ.
- z = ±1.96 — 95% confidence boundary (two-tailed p = 0.05).
- z = ±2.58 — 99% confidence boundary (two-tailed p = 0.01).
- z = ±3 — only 0.27% of values are this extreme.
Z-scores require normally distributed data and known population parameters. For sample data with small n, use a t-score instead. Probabilities computed via the Abramowitz-Stegun rational approximation (max error ~10⁻⁷).