Z-Test for Proportions Calculator

About this calculator

The one-sample z-test for a proportion checks whether an observed proportion p̂ (successes divided by sample size n) differs significantly from a hypothesized value p₀. The test statistic is z = (p̂ − p₀) / √(p₀(1 − p₀)/n), which measures how many standard errors the observed proportion sits from the hypothesized one, assuming the null hypothesis is true; it follows a standard normal distribution when np₀ and n(1 − p₀) are both reasonably large (a common rule of thumb is at least 5 or 10).

This test is a workhorse in A/B testing (does a new checkout flow convert at a different rate than the historical baseline?), quality control (is the defect rate still at the target 2%?), and survey or clinical research (does the observed response rate match an assumed population rate?). Enter the number of successes, the sample size, and the hypothesized proportion, and the calculator returns z along with the observed proportion p̂ for comparison.