Critical Value Calculator
Critical values for z, t, chi-square, or F at any alpha and tail.
About this tool
Pick a distribution, enter alpha, df where needed and the tail. The critical value is shown with the density curve and shaded rejection region.
How to use
How it works
The critical value is the test statistic boundary of the rejection region. For a two-tailed test it uses alpha ÷ 2 in each tail. Choose the distribution that matches your test: z or t for means, chi-square for counts and variances, F for variance ratios and ANOVA.
critical value = quantile of the distribution at 1 − α (right) or 1 − α/2 (two-tailed)
Worked example
t with 20 degrees of freedom
- Input
- t, df = 20, α = 0.05, two-tailed
- Output
- 2.086
- Walkthrough
- The same α gives z 1.645 (right-tailed), chi-square df 5 = 11.070, and F(2, 30) = 3.316.
Limitations
- Gives the cut-off; it does not run the hypothesis test.
- Exact values may differ in the last digit from rounded textbook tables.
Questions
What is the t critical value for 20 df?
What is the z critical value for right-tailed 0.05?
What is the chi-square critical value for df 5?
What is the F critical value for df 2 and 30?
Features
- Four distributions
- Shaded curve
- Runs in your browser
Guides
Related resources
Guides and videos from around the web—opens on YouTube or the publisher’s site.
Student's t-distribution
Khan Academy
Why t-tables differ from z for small samples.
Watch on YouTubeChi-square distribution introduction
Khan Academy
Background for χ² tables and GoF/independence tools.
Watch on YouTube
- Introductory Statistics
OpenStax
Free textbook for hypothesis tests and tables.
- Student's t-distribution
Wikipedia
Distribution reference behind the t-table tool.