Statistics Calculators

P-Value Calculator (from Z-Score)

Calculate the p-value corresponding to a z-score for a left-tailed, right-tailed or two-tailed hypothesis test.

P-value —

P-value (percentage) —

About the P-Value Calculator (from Z-Score)

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated — assuming the null hypothesis is true. Smaller p-values provide stronger evidence against the null hypothesis.

Formula: Left-tailed: p = Φ(z) · Right-tailed: p = 1 − Φ(z) · Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z)), where Φ is the standard normal cumulative distribution function

A p-value below a chosen significance threshold (commonly 0.05) is typically considered statistically significant, meaning the result is unlikely to have occurred by chance alone under the null hypothesis.