P-Value Calculator From Statistic to Significance
Turn a z, t, chi-square, or F statistic into its exact p-value — with the tail convention made explicit and a significance verdict at your alpha.
Exact distributions
The kernels evaluate the real CDFs (Numerical Recipes algorithms), matching published critical-value tables to six decimals.
Statistic in, p-value out
This tool converts an existing statistic — compute t or z first with our companion calculators.
What is a p-value?
The tail probability of your test statistic
A p-value is the probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one your study produced. This calculator converts a ready-made z, t, χ², or F statistic into that probability — the last step of almost every hypothesis test.
The p-value is a tail area under the statistic's null distribution. For a right-tailed test it is everything above your statistic; for a left-tailed test everything below it; a two-tailed test doubles the outer tail. According to the NIST/SEMATECH e-Handbook of Statistical Methods, this tail-area definition is the standard convention for reporting test results, and the underlying distribution functions follow the classic formulas in Abramowitz & Stegun.
p = 2 × (1 − F(|x|))For the asymmetric χ² and F distributions the two-tailed value doubles the smaller of the two tails, capped at 1. The α level you select never changes the p-value — it only sets the threshold for the significance verdict.
Evaluate the distribution at your statistic
For z = 1.96 the standard normal CDF gives Φ(1.96) = 0.9750 — 97.5 % of the distribution lies below your statistic.
Apply the tail convention
Two-tailed doubles the outer tail: p = 2 × (1 − 0.9750) = 0.0500.
Compare against α
With α = 0.05 the result sits exactly on the boundary: p = 0.0500 is not below 0.05, so it is not significant by a hair.
Keep in mind that the p-value measures surprise under the null hypothesis, nothing more. According to the American Statistical Association's 2016 statement, a p-value is not the probability that the null hypothesis is true, and it says nothing about the size or practical importance of an effect — a tiny p can accompany a trivially small effect in a large sample.
Accuracy and scope
Results are for informational purposes and assume your statistic was computed correctly and its distributional assumptions hold (normality, independence, correct degrees of freedom). This tool converts an existing statistic; it does not check your study design. Degrees of freedom are validated as whole numbers from 1 to 1,000.