Use this p-value calculator to compute tail probability for a known test statistic. Supports normal, t, chi-squared, and F distributions with one-tailed and two-tailed options.
Use template ->What is a p-value?
A p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. It is the primary output of most frequentist statistical tests and is used to assess whether observed data provides sufficient evidence to reject the null hypothesis at a chosen significance level.
The conventional threshold of 0.05 means that results at that level would occur by chance in about 5% of experiments if the null were true. But the p-value should be understood as a continuous measure of evidence, not a binary pass/fail. A value of 0.049 and a value of 0.051 represent essentially the same strength of evidence, even though one crosses the threshold and the other does not.
How p-values are calculated
For a one-tailed test: p = P(test statistic ≥ observed value | H₀ is true)
For a two-tailed test, the p-value is doubled to account for both tails.
The precise calculation depends on the distribution of the test statistic and the degrees of freedom where applicable. Normal and t distributions are used for means and regression coefficients; chi-squared for goodness-of-fit and independence tests; F for variance ratios and ANOVA.
How the p-value calculator works
The calculator takes a test statistic and distribution parameters as inputs and returns the tail probability directly. Distribution choice and tail direction are explicit inputs rather than defaults, because those choices materially affect the output and are a common source of interpretation error in practice.
The CDF and survival function outputs serve as a cross-check, particularly for non-symmetric distributions where intuition about tail probabilities tends to be less reliable.
How p-values are used in statistical inference
P-values appear in hypothesis testing across every quantitative discipline: medical research, A/B testing, econometrics, quality control, social science research. The p-value should always be read alongside effect size, sample size, and test context, because statistical significance and practical significance are not the same thing. A very large sample can produce a statistically significant result from a practically irrelevant difference, which is why the number alone is rarely sufficient for a complete interpretation.