P-value Calculator
Convert a test statistic into a p-value for the z, t, chi-square, or F distribution, with one- and two-tailed options and an automatic significance check at α = 0.05.
FreeNo sign-upPrivate — runs in your browser, nothing is uploaded
At α = 0.05 this result is statistically significant (reject H₀).
Computed in your browser using the regularized incomplete gamma and beta functions (accurate to ~6 significant figures). Two-tailed p-values assume a symmetric test.
Quick answer
A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. Enter your statistic, pick the distribution (normal z, Student's t, chi-square, or F) and the tail, and this calculator returns the p-value using the regularized incomplete gamma and beta functions — accurate to about six significant figures. A p-value below your significance level (commonly 0.05) means the result is statistically significant.
Formula & method
The normal (z) p-value uses the error function: the two-tailed value is 2·(1 − Φ(|z|)). The t and F p-values use the regularized incomplete beta function, and the chi-square p-value uses the regularized incomplete gamma function. These special functions are evaluated with the standard series and continued-fraction expansions (Numerical Recipes), giving ~6 significant figures of accuracy.
Examples
- Input
- Normal (z), 1.96, two-tailed
- Result
- p ≈ 0.05
- Why
- 1.96 is the classic 5% critical value: 2·(1 − Φ(1.96)) = 0.0500.
- Input
- Student's t, 2.131, df = 15, two-tailed
- Result
- p ≈ 0.05
- Why
- t = 2.131 is the two-tailed 5% critical value for 15 degrees of freedom.
- Input
- Chi-square, 3.841, df = 1, right tail
- Result
- p ≈ 0.05
- Why
- χ² = 3.841 with 1 df is the 5% critical value, so the upper-tail p-value is 0.05.
When to use this tool
- Reporting significance after a t-test, ANOVA, chi-square, or z-test.
- Checking a statistic against a textbook critical-value table.
- Teaching or learning how test statistics map to p-values across distributions.
Common mistakes
- Confusing one-tailed and two-tailed tests — a two-tailed p-value is roughly double the one-tailed value for the same statistic.
- Forgetting the degrees of freedom for the t and chi-square tests, or swapping the numerator and denominator df for the F test.
- Reading a p-value as the probability that the null hypothesis is true — it is not; it is the probability of the data given the null.
Frequently asked questions
What counts as statistically significant?
By convention, a p-value below the significance level α (often 0.05) is called statistically significant, meaning you reject the null hypothesis. The tool flags this automatically at α = 0.05.
One-tailed or two-tailed — which should I use?
Use a two-tailed test when you care about a difference in either direction, and a one-tailed test only when your hypothesis is directional. Choose the matching option before reading the p-value.
How accurate is the result?
About six significant figures. It uses the regularized incomplete gamma and beta functions rather than a lookup table, so values between table rows are exact.
What degrees of freedom do I enter?
For a t or chi-square test, enter its df. For an F test, enter the numerator df₁ and denominator df₂ separately, in that order.
Does a small p-value prove my hypothesis?
No. A small p-value is evidence against the null hypothesis, but it does not measure effect size or prove the alternative. Always report it alongside the effect and context.
Is my data uploaded?
No — only the single statistic you type is used, and all computation happens in your browser.
Sources & references
External references open in a new tab. We are independent and not affiliated with these organizations.
- ✓ Free to use
- ✓ No sign-up required
- ✓ Runs entirely in your browser — nothing is uploaded.
- ✓ Formula and method shown above
Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
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