🧮 P-Value Calculator
Turn a test statistic — z, t, chi-square or F — into a p-value, one-tailed or two-tailed, using exact distribution functions.
p-value
0.049996
p ≤ α — statistically significant, reject H₀
Exact p-values from the cumulative distribution functions (erf, regularized incomplete gamma & beta). 🔒 Computed in your browser.
How the p-value calculator works
Choose the distribution your test statistic comes from, enter the statistic (and degrees of freedom for t, χ² and F), and the tool returns the p-value from the exact cumulative distribution function. For z and t you can pick a left, right, or two-tailed alternative; χ² and F tests are right-tailed. A verdict compares the p-value to your significance level (α).
The exact special functions (error function, regularized incomplete gamma and beta) are the same ones behind statistical software — so the p-value is precise, not a table approximation that a chatbot would round or get wrong.
Frequently asked questions
How do I convert a z-score to a p-value?
The p-value is the tail area beyond the statistic. For a right-tailed z-test it is P(Z > z); for two-tailed it is 2 × P(Z > |z|). Choose the distribution "z" and your tail, and the tool computes it exactly.
What is a p-value?
The probability of observing a test statistic at least as extreme as yours if the null hypothesis were true. A small p-value (typically ≤ 0.05) is evidence against the null hypothesis.
When is a result statistically significant?
When the p-value is at or below your chosen significance level α (commonly 0.05). This tool shows the verdict — reject or fail to reject the null hypothesis — against your α.
What is the difference between one-tailed and two-tailed?
A one-tailed test looks for an effect in a single direction (only larger, or only smaller); a two-tailed test looks for any difference. Two-tailed p-values are double the one-tailed value for symmetric distributions.
Which distribution should I choose?
z for large-sample or known-variance tests, t for small-sample mean tests (with degrees of freedom), χ² for goodness-of-fit and independence tests, and F for ANOVA and variance ratios.
Why not just read a table?
Tables are coarse and require interpolation; this computes the exact p-value for any statistic and degrees of freedom, with no rounding — and it runs entirely in your browser.
Related statistics tools
From the blog
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The t-Test Explained: One-Sample, Two-Sample and Paired
A t-test answers one question: is a difference in means real, or could it be chance? Here's how the three types work, how to pick between Welch and pooled, what the p-value actually tells you, and the mistake almost everyone makes reading a non-significant result.
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Z-Score to P-Value: How to Read the Normal Distribution
A p-value is the tail area of the normal curve beyond your z-score. z = 1.96 gives a two-tailed p of 0.05; z = 1.645 a one-tailed p of 0.05. How the conversion works, one- versus two-tailed, and why a table is coarser than the exact erf calculation.