p value calculator
Convert a test statistic into a p value, or turn a significance level back into the critical value to compare against.
The two directions people need
You have a test statistic from software or a hand calculation and need the p value. Or you have a significance level and need the critical value to compare against. This page does both, for the four distributions that cover nearly every classical test.
Worked values to check against
| Input | Result |
|---|---|
| t = 2.50, df = 20 | two-tailed p = .021 (one-tailed .011) |
| F = 3.50, df = 2, 30 | p = .043 |
| χ² = 5.00, df = 2 | p = .082 |
| t critical, α = .05 two-tailed, df = 20 | 2.0860 |
| χ² critical, α = .05, df = 2 | 5.9915 |
| F critical, α = .05, df = 2, 30 | 3.3158 |
These come from the same distribution code the application uses, which is cross-checked against published tables and numerical integration — see the verification record.
Tails are not symmetric across tests
For t and z the two-tailed p value is twice the upper tail of the absolute statistic, because the distribution is symmetric and either direction counts as evidence. For F and chi-square the test is one-tailed by construction: large values are the only evidence against the null, so there is no second tail to add.
Reporting "two-tailed" for an F test is a sign the value was computed mechanically rather than understood.
Reading a p value correctly
A p value is the probability of data at least this extreme if the null hypothesis were true. It is not the probability that the null is true, and it is not the probability that you made an error. A small p value says the data are unlikely under the null; it says nothing about how large the effect is.
Report the effect size and a confidence interval next to it. A p value alone answers a question nobody asked.
Frequently asked
Which tail does my software report?
Most regression output and most t test procedures report two-tailed p values. ANOVA tables report one-tailed F. If a value looks exactly half of what you expected, check the convention.
Can I get the p value from a correlation?
Yes — t = r√(n−2) / √(1−r²) with n−2 degrees of freedom, which is what the correlation calculator does internally.
My p value is exactly .05. Significant?
The threshold is a convention, not a fact. A value on the line means the evidence is marginal, and the effect size should decide how you describe it.
Is my input uploaded?
No. Everything is computed in JavaScript on this page.
From a p value to a whole table
The app runs the procedure, checks its assumptions, and exports the formatted table with the APA sentence — including the degrees of freedom and the effect size, which is what a reader actually needs.
Which test should I use? · t test calculator · chi-square calculator · ANOVA calculator · correlation calculator · p value calculator