P-Value Calculator

Compute a p-value for a z-test or t-test.

Distribution
How to provide the statistic
Tails

Two-tailed p-value (z-test)

0.049996

Test statistic: 1.96

Statistically significant at α = 0.05

How the p-value works

The p-value is the probability of observing a test statistic at least as extreme as the one you obtained, assuming the null hypothesis is true. It is not the probability that the null hypothesis is correct.

This calculator supports two defensible tests: the z-test (standard normal) and the t-test (Student's t with degrees of freedom). For a z-test you can enter the z statistic directly, or compute z from a one-proportion test.

Compare the p-value to your significance level (α, commonly 0.05). If p < α the result is statistically significant. Statistical significance is not the same as practical importance, and a significant result does not prove a real-world effect.

The formulas

z = (p̂ − p₀) ÷ √(p₀(1−p₀) ÷ n) · two-tailed p = 2·P(|Z| ≥ |z|)

For a one-proportion z-test, z compares the observed proportion to a hypothesized value. The p-value is then read from the normal or t distribution according to the tails you select.

Worked example

A z-test at the 5% level

If your computed z is 1.96, the two-tailed p-value is 0.05 — exactly at the conventional 5% significance level. A z of 2.58 gives p ≈ 0.01.

Frequently asked questions

What is the difference between one-tailed and two-tailed?

A two-tailed test checks for a difference in either direction; a one-tailed test checks only for an increase (upper) or only for a decrease (lower). Two-tailed is the common default.

What does statistical significance mean?

It means the observed result is unlikely under the null hypothesis at your chosen level. It does not mean the effect is large, important, or causal — that is practical significance, judged separately.

Can I always get a p-value from any statistic?

No. A p-value is only meaningful for a defined test with stated assumptions. This calculator supports the normal and t distributions; using the wrong distribution for your test gives a misleading result.

Built by PanelRoster

PanelRoster is an enterprise operations management platform for organizations coordinating distributed teams, assignments, workflows, quality assurance and operational execution.

Explore PanelRoster