Convert between raw scores, z-scores, cumulative probability, and confidence intervals on the standard normal distribution — useful for A/B tests, hypothesis testing, and quick sanity checks.
Standardize a raw score x given population mean μ and stddev σ: z = (x − μ) / σ.
Compute the p-value (cumulative probability) for a given z-score.
Find the z-score (critical value) for a given probability.
Confidence interval for a sample mean using the normal approximation: x̄ ± z × (σ/√n).
A z-score measures how many standard deviations a value sits above or below the mean. The standard normal CDF Φ(z) gives the probability that a standard normal variable is less than z. This calculator uses a rational-polynomial approximation (Abramowitz & Stegun 26.2.17) accurate to ~7 decimal places for |z| ≤ 6, and the Beasley-Springer-Moro algorithm for the inverse.