Choose the reference distribution and tail
A z statistic is compared with the standard normal distribution. A t statistic is compared with Student’s t distribution using the degrees of freedom of the underlying test. This tool converts an already computed statistic; it does not decide which test fits your data.
If F is the cumulative distribution function, left-tail probability is F(s), right-tail probability is 1 − F(s), and the two-tailed value for these symmetric distributions is twice the smaller tail. Choose the alternative hypothesis before observing the result.
A worked normal example
For z = 1.96, the left-tail area is about 0.9750021, the right-tail area is about 0.0249979, and the two-tailed p-value is about 0.0499958. A two-tailed comparison with a preselected 0.05 significance level just meets that threshold.
In reverse mode, a normal two-tailed probability of 0.05 corresponds to a magnitude of about 1.959963985. Both positive and negative statistics of that magnitude have the same two-tailed area. Central-area modes show probability coverage, not hypothesis-test p-values.
Interpreting the output
A p-value describes how extreme a result would be under the null model and the test’s assumptions. It is not the chance that the null hypothesis is true, the probability an effect is important, or a substitute for effect size and study design.
The implementation computes small tails directly to avoid subtraction loss and numerically inverts the selected region. Inverse probabilities are supported from 10^-12 to 1 − 10^-12; Student t supports 1–10,000 whole degrees of freedom. Extreme forward tails can fall below floating-point precision.