The common search intent behind a P value calculator is practical: is the difference between a sample mean and a reference value too large to explain by ordinary random variation? This page answers that question in one defined setting: a one-sample, two-tailed z test using a sample mean, null mean, population standard deviation, and sample size.
After you enter the summary statistics, the page shows a z statistic, a two-tailed P value, and a fixed-threshold interpretation. It is useful for introductory statistics, class exercises, formula checks, and quick approximations. It is not a general statistical package. Use the Z-Score Calculator to check standardized scores, the Probability Calculator for basic probability work, or the Scientific Calculator for general mathematical follow-up.
If you only have a sample standard deviation, need a t distribution, need a one-tailed test, need a custom α, or need a proportion, variance, contingency-table, or multi-group test, use a tool that supports that test explicitly.
Enter the average of the observed sample. It can be positive, negative, or zero, but its unit must match the null mean and standard deviation.
It runs a one-sample, two-tailed, normal-approximation z test from summary statistics; it does not offer one-tailed choices or t, chi-square, or F distributions.
The formula uses σ/√n as the standard error and assumes σ is known; if you only have a sample standard deviation, a t test with degrees of freedom is usually more appropriate.
With a preselected α = 0.05 and reasonable model assumptions, it is commonly used to reject the null; it does not mean the effect is large or that the null has a 5% chance of being true.
You cannot enter α here; the interpretation bands use fixed 0.01, 0.05, and 0.10 thresholds, while the bottom conclusion always compares with 0.05.
The result card formats P values to six decimal places, so a tiny positive value can display as 0.000000; that does not mean the mathematical P value is exactly zero.
Calculate the z statistic and two-tailed P value for a one-sample z test from a sample mean, null mean, population SD, and sample size.