P-Value from Z-Score Calculator

About this calculator

This calculator converts a z-score into a p-value using the cumulative distribution function of the standard normal distribution. The one-tailed p-value is the probability of observing a value at least as extreme as the z-score in one direction (Φ(−|z|)), while the two-tailed p-value doubles that to account for extremes in either direction — the value most commonly compared against a significance threshold like α = 0.05.

Researchers, statisticians, and students use this conversion as the final step of a hypothesis test: after computing a test statistic (from a z-test, a large-sample proportion test, etc.), the z-score is translated into a p-value to decide whether to reject the null hypothesis. A p-value below the chosen significance level indicates the observed result would be unlikely under the null hypothesis, and is conventionally treated as statistically significant.