P-value Calculator
Calculate p-values for z-tests, t-tests, and chi-square tests. Includes significance testing interpretation.
| α Level | Z Critical | Decision |
|---|---|---|
| 0.10 | ±1.645 | Reject if |z| > 1.645 |
| 0.05 | ±1.960 | Reject if |z| > 1.960 |
| 0.01 | ±2.576 | Reject if |z| > 2.576 |
| 0.001 | ±3.291 | Reject if |z| > 3.291 |
Find the p-value for a Z-test, t-test, or chi-square test from your test statistic, and instantly see whether the result is statistically significant at common alpha levels.
How P-value Calculator Works
For a Z-test, the calculator uses a standard normal cumulative distribution approximation to find the probability of observing a value at least as extreme as your z-statistic. A two-tailed test doubles the smaller tail probability; a one-tailed (left or right) test uses just that one side directly.
For a T-test, you also supply the degrees of freedom (df). The calculator converts the t-statistic toward an equivalent z-value using t/√(1 + t²/(2·df)) and then applies the same normal-distribution approximation — this is a fast approximation that tracks the exact Student's t-distribution closely for larger df, though it becomes slightly less precise for very small df.
For a Chi-square test, the p-value is the upper tail of the chi-square distribution — computed as 1 minus the regularized incomplete gamma function evaluated at your chi-square statistic and degrees of freedom. In every mode, the resulting p-value is compared against α = 0.10, 0.05, and 0.01 to flag significance at each common threshold.
See It In Action
Who Uses P-value Calculator and Why
- Checking whether a Z-test statistic from a study reaches statistical significance at the standard 0.05 level.
- Evaluating a t-test result from a small-sample experiment using the supplied degrees of freedom.
- Determining the significance of a chi-square goodness-of-fit or independence test statistic.
- Comparing a computed p-value against multiple alpha thresholds (0.10, 0.05, 0.01) at once to see how strong the evidence really is.
Mistakes to Avoid
- Choosing a one-tailed test after already seeing which direction the data leans — the choice between one-tailed and two-tailed should be made based on the hypothesis before looking at results, not after.
- Treating a very small p-value as proof of a large or practically important effect — p-values measure evidence against the null hypothesis, not the size of the effect itself.
- Forgetting to supply the correct degrees of freedom for a t-test or chi-square test — both distributions change shape with df, which directly changes the resulting p-value.
Tips for Best Results
- Decide one-tailed versus two-tailed based on what your hypothesis actually predicts, and commit to that choice before running the test.
- Check the p-value against all three common alpha levels (0.10, 0.05, 0.01) shown, rather than only the 0.05 cutoff, to see how robust the significance really is.
Fixing Common Problems
My t-test p-value seems slightly off from a textbook table. — This calculator uses a fast normal-distribution approximation for the t-test that tracks the exact Student's t-distribution closely for larger degrees of freedom but is slightly less precise for very small df.
I'm not sure whether to run a one-tailed or two-tailed test. — Use two-tailed if you're testing for any difference in either direction; use one-tailed only if your hypothesis specifically predicts a difference in one particular direction, decided before seeing the data.
Terms Explained
Null hypothesis: The default assumption of no effect or no difference that a p-value measures evidence against.
Degrees of freedom: A value reflecting how much independent information went into a statistic, which affects the shape of the t- and chi-square distributions used to compute a p-value.