P-Value and Critical Value Calculator for z, t, Chi-Square, F and r
Got a test statistic from a paper or your software and need the exact p-value? Or need the critical value without hunting through tables? Pick the distribution, enter the numbers and see the shaded area on the curve.
How to use the P-Value Calculator
- Choose Statistic → p-value to get a p-value, or α → critical value for the cut-off from a statistics table.
- Select the distribution (z, t, χ², F or r) and enter the degrees of freedom. For r, enter the sample size n.
- Choose two-tailed (most tests) or one-tailed. χ² and F tests are right-tailed by nature.
- Enter your test statistic or α. The result and the shaded curve update as you type.
What is a p-value?
A p-value is the probability of getting a result at least as extreme as yours if the null hypothesis were true. A small p-value (for example below 0.05) means your data would be surprising under the null hypothesis, so you reject it. A p-value is not the probability that the null hypothesis is true, and it says nothing about how big or important an effect is. Report an effect size alongside it.
Which distribution do I need?
| Test | Statistic | Degrees of freedom |
|---|---|---|
| z-test, large-sample proportions | z | – |
| t-tests, regression coefficients | t | n − 1, n₁ + n₂ − 2, or Welch df |
| Chi-square tests | χ² | (rows − 1)(columns − 1), or k − 1 |
| ANOVA, regression F-test | F | df between, df within |
| Pearson correlation | r | enter n (df = n − 2) |
How accurate is it?
The calculator uses the regularized incomplete beta and gamma functions, the same mathematics used inside R, SPSS and Excel’s T.DIST and CHISQ.DIST functions. Results agree with R to at least six decimal places, including very small p-values.
Frequently asked questions
How do I get a p-value from a t value?
Choose the t distribution, enter the degrees of freedom and your t value, and keep two-tailed selected unless you had a directional hypothesis. For example, t(20) = 2.1 gives p = .049 (two-tailed).
What is the critical value of t at 0.05?
It depends on the degrees of freedom. For a two-tailed test at α = 0.05 it is 2.228 with 10 df, 2.086 with 20 df, 2.042 with 30 df, and approaches 1.960 as df grows. Use the critical value tab for any df.
Should I use a one-tailed or two-tailed p-value?
Two-tailed is the default in almost all research. Use one-tailed only when you stated the direction before collecting data, and never switch after seeing the results just to get p < .05.
Why can't χ² and F tests be two-tailed here?
Chi-square and F statistics are squared quantities, so large values in the right tail already capture differences in any direction. They are evaluated in the right tail.
How do I write very small p-values?
In APA style, write p < .001 for anything smaller than 0.001 rather than the exact value. Never write p = .000.
Is anything sent to a server?
No. All calculations run in your browser.