Summary: This p value calculator computes Z, t, chi-square and F tests with live steps, formulas and a chart. It accepts labeled numeric inputs, works offline through file:// and includes source-backed explanations for students, analysts and researchers.
P value calculator from Z, t, chi-square and F statistics with one-tailed and two-tailed results, formulas and interpretation. The calculator works offline, updates instantly and includes a worked example, plain-text formula, MathML, references and structured data.
Default values are loaded. Click any field and edit it; results and chart update automatically.
| Input or setting | Result or interpretation | Use this when |
|---|---|---|
| z=1.96 two-tailed | p about 0.0500 | tail probability |
| z=2.576 two-tailed | p about 0.0100 | tail probability |
| chi-square=5, df=2 | p about 0.082 | tail probability |
two-tailed Z: p = 2 * (1 - Phi(abs(z))); right-tailed chi-square: p = 1 - F(chi-square)A p-value is the probability of a result at least as extreme under the null hypothesis and model assumptions.
z = 1.96, two-tailed
p about 0.0500
This page uses the shared statistics core for distribution functions, quantiles and exact integer counting where needed. The formula is shown in plain text so screen readers and search engines can parse it reliably.
Use Load example in the calculator to reproduce this reference result.
{
"tool": "P Value Calculator",
"input": "z = 1.96, two-tailed",
"output": "p about 0.0500",
"formula": "two-tailed Z: p = 2 * (1 - Phi(abs(z))); right-tailed chi-square: p = 1 - F(chi-square)"
}| Calculator | Example input | Expected output |
|---|---|---|
| P Value Calculator | z = 1.96, two-tailed | p about 0.0500 |
What does p = 0.03 mean? If the null hypothesis and model assumptions were true, a result at least this extreme would occur about 3% of the time. The American Statistical Association cautions that a p-value alone does not measure effect size, practical importance or the probability that Hâ‚€ is true.3
For most classroom and professional reports, pair the calculator result with the question you are answering. A mean or median summarizes location, but spread explains consistency. A confidence interval estimates plausible values, while a hypothesis test evaluates compatibility with a null model. Regression and correlation describe association, so they should be reported with a chart and residual or outlier review. When a result is statistically significant, still ask whether the effect is large enough to matter in the real setting.
| Statistic | Small | Medium | Large | Use |
|---|---|---|---|---|
| Cohen's d | 0.2 | 0.5 | 0.8 | t-test effect size |
| Cramér's V | 0.1 | 0.3 | 0.5 | chi-square association |
| |r| | 0.10 | 0.30 | 0.50 | correlation strength |
| R² | 0.01 | 0.09 | 0.25 | variance explained |
Use the standard normal distribution. For a one-tailed test, the p-value is the area in one tail beyond your z. For a two-tailed test, it's twice that area. Suppose z = 2.0 and you're running a right-tailed test: p = P(Z > 2.0) ≈ 0.0228. For two-tailed, p ≈ 2 × 0.0228 ≈ 0.0456. In Excel, =1-NORM.S.DIST(2, TRUE) gives the right tail. The tail you choose depends on your alternative hypothesis — direction matters, so set it up before you collect data.
You need three inputs: the t value, the degrees of freedom, and whether the test is one- or two-tailed. The p-value is the area in the appropriate tail (or tails) of the t distribution beyond your computed t. Example: t = 2.5 with df = 20 in a two-tailed test gives p ≈ 0.021. Software handles this instantly — Excel's T.DIST.2T(2.5, 20) returns 0.0214. Larger df makes the t distribution closer to normal. Without software, you'd interpolate from a t-table to find approximate p-value bands.
A one-tailed p-value tests whether your statistic falls in one specific direction — say, "is the new drug better than the old?" Only the upper or lower tail counts. A two-tailed p-value tests whether the statistic differs from the null in either direction — "does the drug change outcomes, up or down?" The two-tailed p is roughly twice the one-tailed for symmetric distributions. Pick one-tailed only when you have a clear directional hypothesis before seeing data; otherwise stick with two-tailed for honest, conservative inference.
A p-value below 0.05 means that, assuming the null hypothesis is true, your observed result (or something more extreme) would happen less than 5% of the time by chance. So you reject H0 at the 0.05 significance level. Important caveat: p < 0.05 does not mean H0 has only a 5% chance of being true — that's a common but wrong interpretation. The 5% threshold is conventional, not magical. A p of 0.049 and 0.051 carry essentially the same evidence, despite landing on opposite sides of the line.
The chi-square distribution is right-skewed and lives only on positive values, so the p-value is always the right-tail area beyond your computed χ². Example: χ² = 7.815 with df = 3 gives p ≈ 0.05 (a familiar critical value). In Excel, =CHISQ.DIST.RT(7.815, 3) returns the p-value directly. Higher χ² with the same df means a smaller p-value and stronger evidence against H0. The shape of the distribution depends on df — small df means a sharply right-skewed curve; large df flattens out toward symmetry.
F-tests use the F distribution, which has two parameters: numerator df and denominator df. Like chi-square, F is non-negative, and the p-value is the right-tail area beyond your F statistic. Example: F = 4.50 with df1 = 3, df2 = 20 gives p ≈ 0.014 in Excel via =F.DIST.RT(4.5, 3, 20). Higher F means more variation between groups relative to within — and a smaller p-value. F-tests show up in ANOVA, regression overall significance, and variance comparisons. Both df values must be specified correctly.
No, never. A p-value is a probability, so it must lie between 0 and 1 inclusive. If you ever see a value above 1 — or below 0 — there's an error somewhere: wrong formula, mistyped statistic, swapped numerator and denominator, or a bug in the code. Common mistake: doubling a one-tailed p that's already greater than 0.5 to get a two-tailed value above 1. The correct approach for two-tailed is 2 × min(P(T ≥ t), P(T ≤ t)), which keeps you safely under 1.
The p-value tells you how compatible your data are with the null hypothesis. Small p-values (typically < 0.05) suggest the data would be unlikely under H0, leading you to reject it. Larger p-values mean the data are consistent with H0 — but that doesn't prove H0 is true, only that you lack evidence to reject it. Always pair the p-value with effect size and a confidence interval — a tiny effect can be statistically significant in huge samples, while a meaningful effect can fail significance in small ones.